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Really? Gosh!

QL-development seems to be a search for the most efficient destruction of the entire series.

So I can understand these changes.

So I can understand these changes.

By juan_juanson - Reply to #2

A lot of the Steam launch changes were unpopular and I don't blame anyone for being pissed off. These changes, though, could be a good thing.

By asdfasdfasdf - Reply to #37

so you're just an intellectual bully?

Bullying is something by which you attack a person, I attack decisions and possible logic behind the decisions / views.

I can also praise decisions, although I don't usually do that online as it doesn't attribute anything new. Whereas disagreeing does give 'a different view'.

I have been known to sometimes support good decisions as well though, especially ones which were attacked by the community for no good reason.

I can also praise decisions, although I don't usually do that online as it doesn't attribute anything new. Whereas disagreeing does give 'a different view'.

I have been known to sometimes support good decisions as well though, especially ones which were attacked by the community for no good reason.

By asdfasdfasdf - Reply to #41

nice justification for your aggressive campaign of abuse.

By asdfasdfasdf - Reply to #45

it's typical of defensive aggressors to stall for time when responding to interrogative accusations by repeating the questions.

Edited by brandan at 17:22 CST, 25 November 2014

By asdfasdfasdf - Reply to #52

and now you attempt to distract from the assertion of your bullying by asking irrelevant questions. do you really believe that people can't see through this fragile facade?

By asdfasdfasdf - Reply to #55

your condescending arrogance blinds you to the judgmental capabilities of others. your parade of hateful vendetta marches blindly through the main streets of others perceptions. the only thing your 'intelligence' serves to convince is yourself of your own desires. this is irony.

look at brandan all grown up.

He now attempts to troll using difficult words!

You know, if you don't have anything to say except making vague seemingly random accusations and allegations perhaps you should go back into your rock.

It's fun to see you trying though... so you can stick around and google some more synonyms :D

He now attempts to troll using difficult words!

You know, if you don't have anything to say except making vague seemingly random accusations and allegations perhaps you should go back into your rock.

It's fun to see you trying though... so you can stick around and google some more synonyms :D

By asdfasdfasdf - Reply to #63

and now come the personal attacks. i understand that this behavior becomes habitual, and that the practice of habitual behaviors can be comforting in their familiarity, but a key aspect of intelligence is a capacity to predict consequences over spans of time. this negative behavior not only contributes to the short-term chemical rewards that get you through your day, but also to the long-term chemical structures inhibiting your ability to function in social situations.

it is my sincere hope that you will somehow assume the strength to see beyond your egotistically shortsighted deferments of personal responsibility for your future health, so that you may accept that responsibility and begin to work toward a brighter future for yourself, and through your selfish improvement, a brighter future for others.

it is my sincere hope that you will somehow assume the strength to see beyond your egotistically shortsighted deferments of personal responsibility for your future health, so that you may accept that responsibility and begin to work toward a brighter future for yourself, and through your selfish improvement, a brighter future for others.

actually the personal attack started here:

your condescending arrogance blinds you....

And before that you make false accusations about me.

When people insult me it's fair game to do the same back m8.

I won't let you bully me around like you do with others. I'm too smart for that :D

your condescending arrogance blinds you....

And before that you make false accusations about me.

When people insult me it's fair game to do the same back m8.

I won't let you bully me around like you do with others. I'm too smart for that :D

By asdfasdfasdf - Reply to #67

i understand the defensiveness that comes from being confronted with your own flawed perception of reality, weird. i have been there, anybody who hasn't is either not human, or too young to have experienced it. describing your condescending arrogance isn't a personal attack, but a sincere attempt to highlight a personal issue that is inhibiting your personal development. i only want what is best for you.

I don't see where you see defensiveness.... It's probably right next to my aggressive campaign of abuse :D

By asdfasdfasdf - Reply to #72

so now we've reached denial, which is natural and expected, but the important and positive fact is that you're also questioning yourself. this is good progress. i'm happy for you.

Edited by brandan at 18:28 CST, 25 November 2014

By asdfasdfasdf - Reply to #74

you can see that i've communicated my understanding of your feelings and statements and position multiple times. i also understand that, in your position, it is sometimes necessary to defer full realization of your own shortcomings by projecting shortcomings on others. these are all requisite components of human progression. we can get through this, weird, together.

By asdfasdfasdf - Reply to #74

it's rare that somebody really *wants* to be a bully, weird. if i were to treat you as though you are a malicious psychopath, you would fight back against me so violently and defensively that all of my attempts would be tainted by your fear of negative criticism.

it's important to remember that, even if some aspect of your personality is a source of bullying, that it doesn't define you as a person. what will define you as a person is how you handle that personality trait when you are exposed to it.

will you choose to better yourself now, so that your future self will reap the benefits, or will you continue to ignore this opportunity for personal progress, so that you may be cursing your younger self later in life?

the decision is yours, weird, but if i didn't see your potential i would not spend my valuable time to bring this to your attention. :)

it's important to remember that, even if some aspect of your personality is a source of bullying, that it doesn't define you as a person. what will define you as a person is how you handle that personality trait when you are exposed to it.

will you choose to better yourself now, so that your future self will reap the benefits, or will you continue to ignore this opportunity for personal progress, so that you may be cursing your younger self later in life?

the decision is yours, weird, but if i didn't see your potential i would not spend my valuable time to bring this to your attention. :)

Edited by brandan at 18:44 CST, 25 November 2014

By asdfasdfasdf - Reply to #78

extreme words such as 'never' are common indicators for codependent attachment to fantasy, often anchored in a fear of change rooted in that comfort of habitual familiarity i previously mentioned.

You might be right about that.

I was asked to be a local politician a few times but I refused as I don't see myself as good candidate. The current local politicians seem to think I would be though... and I would like to attribute to the quality of life of others.

But my problem is that I can't deal with ignorance... And well... let's face it... there is enough of that even in the national government... it'll be even worse in the local government ;(

I was asked to be a local politician a few times but I refused as I don't see myself as good candidate. The current local politicians seem to think I would be though... and I would like to attribute to the quality of life of others.

But my problem is that I can't deal with ignorance... And well... let's face it... there is enough of that even in the national government... it'll be even worse in the local government ;(

"Bullying is something by which you attack a person, I attack decisions and possible logic behind the decisions / views."- Weird, 25 November 2014

"Dude your like a kid learning how to piss into a toilet. I'm not gonna hold your dick while you ask me retarded questions which are not even needed to be answered."- Weird, 18 March 2013

Edited by obi at 20:27 CST, 26 November 2014

Yes and the guy (was it you?) deserved that.

If I remember correctly this was on the topic of "what mathematicians do" and more specifically on a model (my model :p) for incorperating infinitesimals into math again.

It was one of the most fascenating experiences of someone who argued a point without even having the faintest clue what the hell he was arguing about. Meanwhile the guy wouldn't actually ever think about what I said. Bringing in nonsensical arguments about fields etc :s

It's not my job to teach people who are ignorant. No matter how much they exhibit their ignorance.

If I remember correctly this was on the topic of "what mathematicians do" and more specifically on a model (my model :p) for incorperating infinitesimals into math again.

It was one of the most fascenating experiences of someone who argued a point without even having the faintest clue what the hell he was arguing about. Meanwhile the guy wouldn't actually ever think about what I said. Bringing in nonsensical arguments about fields etc :s

It's not my job to teach people who are ignorant. No matter how much they exhibit their ignorance.

Edited by Weird at 21:44 CST, 26 November 2014

Ah, so its not bullying to attack someone when they "deserve" it. Sounds like a justification a bully would make.

I can't resist: the way you summarised that "debate" is hilariously wrong.

I can't resist: the way you summarised that "debate" is hilariously wrong.

Edited by obi at 01:06 CST, 27 November 2014

rofl.

What is so 'hilariously wrong' about it then?

I do agree that we shouldn't call it a debate.... it was me educating them on how to think.... and them not even attempting to use a single braincell the way it's supposed to be used.

The insight into the field of mathematics exhibited by them was less than I would expect from a monkey.

What is so 'hilariously wrong' about it then?

I do agree that we shouldn't call it a debate.... it was me educating them on how to think.... and them not even attempting to use a single braincell the way it's supposed to be used.

The insight into the field of mathematics exhibited by them was less than I would expect from a monkey.

Ah, so its not bullying to attack someone when they "deserve" it. Sounds like a justification a bully would make.Are you purposefully ignoring the main point of my post?

I don't really want to start that argument again. You are so mathematically ignorant you can't express your ideas clearly, so it just ends up in a circle with you inventing (often contradictory) things on the fly to cover the obvious holes in your "model" (lmao)

There is a "fair" line of "deserving it" and an "unfair" line.

For instance if you kill someone without any reason it's murder and you go to jail. If you however kill someone who attacks you with an axe it's suddenly self defense and you remain free.

Similarly in bullying there is this line.

If I would insult people for no reason it's bullying, however if people come at me with an 'axe of ignorance'. I will point it out as soon as I think it's gotten out of hand.

And in the discussion you are refering to the guy (probably you) came at me with a nuclear bomb of ignorance. So after politely explaining how stupid he was... I eventually made it clear that it's not my job to fix his stupidity.

That someone cannot see the difference between infinity and any arbitrairy extremely high number is not my problem but will forever be his own problem.

For instance if you kill someone without any reason it's murder and you go to jail. If you however kill someone who attacks you with an axe it's suddenly self defense and you remain free.

Similarly in bullying there is this line.

If I would insult people for no reason it's bullying, however if people come at me with an 'axe of ignorance'. I will point it out as soon as I think it's gotten out of hand.

And in the discussion you are refering to the guy (probably you) came at me with a nuclear bomb of ignorance. So after politely explaining how stupid he was... I eventually made it clear that it's not my job to fix his stupidity.

That someone cannot see the difference between infinity and any arbitrairy extremely high number is not my problem but will forever be his own problem.

So after politely explaining how stupid he was... I eventually made it clear that it's not my job to fix his stupidity.Thats exactly your problem. Instead of showing how someone is wrong, or responding logically, you just declare them stupid. You've had this egotistical and childish behaviour pointed out to you several times by different people.

That someone cannot see the difference between infinity and any arbitrary extremely high number...Huh? What the fuck are you talking about?

Edited by obi at 17:57 CST, 27 November 2014

I first explained where the guy was wrong without calling him anything.

It's only after repeated nonsensical (stupid) questions that I make it clear in a more direct maner. I "lower myself to their level" to make it clear. I refer to the 'dude' as a 'kid' for a reason.

The difference between infinity and any arbitraty extremely high number was the concept the other guy didn't get in the thread you're refering to. (iirc)

The reason why this has happened to me before is because I discuss complex issues. Meanwhile I don't see it as my task to "inform others" about all aspects of these issues. I just (sometimes) want to inform people about my views on the issue.

If I express my views on an issue then I do not find it my place to educate everyone who doesn't understand issue in the first place up to such a level that they can understand why my views are right/funny/needed/some other important factor (to me).

If someone would however be able to point out where I'm wrong, then we can have an actual discussion.

But that doesn't happen on esr....

small edit: someone on esr once did point out to me that I had a term confused on a post where I refered to psychology.... So it does happen heheh :D

It's only after repeated nonsensical (stupid) questions that I make it clear in a more direct maner. I "lower myself to their level" to make it clear. I refer to the 'dude' as a 'kid' for a reason.

The difference between infinity and any arbitraty extremely high number was the concept the other guy didn't get in the thread you're refering to. (iirc)

The reason why this has happened to me before is because I discuss complex issues. Meanwhile I don't see it as my task to "inform others" about all aspects of these issues. I just (sometimes) want to inform people about my views on the issue.

If I express my views on an issue then I do not find it my place to educate everyone who doesn't understand issue in the first place up to such a level that they can understand why my views are right/funny/needed/some other important factor (to me).

If someone would however be able to point out where I'm wrong, then we can have an actual discussion.

But that doesn't happen on esr....

small edit: someone on esr once did point out to me that I had a term confused on a post where I refered to psychology.... So it does happen heheh :D

Edited by Weird at 18:13 CST, 27 November 2014

By asdfasdfasdf - Reply to #140

you really should calm down.

It's only after repeated nonsensical (stupid) questions that I make it clear in a more direct maner. I "lower myself to their level" to make it clear.It can't be "their" level when you are the first one to start throwing around insults.

If I express my views on an issue then I do not find it my place to educate everyone who doesn't understand issue in the first place up to such a level that they can understand why my views are right/funny/needed/some other important factor (to me).People don't need educating, they just disagree with you.

If someone would however be able to point out where I'm wrong, then we can have an actual discussion.

Except you will never, ever admit to be wrong about anything important. Its especially funny in Maths because you have been PROVEN wrong but you you don't even understand how (eg the 'irrelevant' Field).

I wasn't PROVEN wrong anywhere except in some further on explanation where I made a typo due to me getting tired of having to re-explain simple concepts. (Which I didn't want to do in the first place)

What happened was that they claimed that I was wrong and then whined that I should prove the opposite.

Which I'm not gonna do for something so trivial that I find any further explanation so boring to do that I make typos.

Proving stuff is a hassle even when it trivial. And it'll be completely over their heads anyway if I did and they would only then not grasp the next concept which I would then have to prove I was right on.

You're more then welcome to present a proof to me that my theory is WRONG and leads to invalid math.

Best of luck.

What happened was that they claimed that I was wrong and then whined that I should prove the opposite.

Which I'm not gonna do for something so trivial that I find any further explanation so boring to do that I make typos.

Proving stuff is a hassle even when it trivial. And it'll be completely over their heads anyway if I did and they would only then not grasp the next concept which I would then have to prove I was right on.

You're more then welcome to present a proof to me that my theory is WRONG and leads to invalid math.

Best of luck.

State it clearly and I'll do it. The reason the argument went on so long is that you never clearly defined it so people are forced to ask about every implication. This isn't asking stupid questions, its trying to pin down exactly wtf you are talking about. The closest we ever got was 'everything is the same, you just allow division by zero' which doesn't work BY DEFINITION.

I never clearly defined it?

Yet somehow the people in the thread came up with proof against my not clearly defined statement?

Interresting...

And you think asking about every implication are not "stupid questions" while I state a very simple rule?

If I remember correctly I said:

x/inf = 0x

0x * inf = x

x - x =

Ofcourse you'd also need:

-x/inf = -0x

And that when you and the other idiot insisted that you needed a symbol for what "is 0 in nowadays math" you are allowed to introduce 0* as a placeholder for x - x = 0* which would be defined as 0 - 0 = 0*.

So in short: you define 0 as a unit infintessimal being 1/inf.

Good luck, see you never.

Yet somehow the people in the thread came up with proof against my not clearly defined statement?

Interresting...

And you think asking about every implication are not "stupid questions" while I state a very simple rule?

If I remember correctly I said:

x/inf = 0x

0x * inf = x

x - x =

Ofcourse you'd also need:

-x/inf = -0x

And that when you and the other idiot insisted that you needed a symbol for what "is 0 in nowadays math" you are allowed to introduce 0* as a placeholder for x - x = 0* which would be defined as 0 - 0 = 0*.

So in short: you define 0 as a unit infintessimal being 1/inf.

Good luck, see you never.

inf = INFINITY

0 = 1 / inf

0* = NOTHING (aka "blank space" but you can't read a 'blank space' as if it is something....)

How is that not obvious?

Would you think I would define it as?

btw.... before you start whining

0x = x / inf.

I say that 0 = 1 / inf because I don't want to write 0x = 1 / inf where x = 1.

And yes the x is important and yes you can get multiples of infinity as well as multiples of 0.

0 = 1 / inf

0* = NOTHING (aka "blank space" but you can't read a 'blank space' as if it is something....)

How is that not obvious?

Would you think I would define it as?

btw.... before you start whining

0x = x / inf.

I say that 0 = 1 / inf because I don't want to write 0x = 1 / inf where x = 1.

And yes the x is important and yes you can get multiples of infinity as well as multiples of 0.

Inf + x = ???

inf + inf = ???

I searched the old thread and didn't see an answer to this.

inf + inf = ???

I searched the old thread and didn't see an answer to this.

Edited by obi at 23:47 CST, 27 November 2014

inf + x = 1/0 + x = x + inf = x + 1/0........

Theres no simplification.

You want to see inf + x = inf because you view inf as "the highest number" but when you do inf + 5 then inf + 5 = the highest number = inf.

But inf is not a number it's a concept, it's abstract, infinity.

To also answer your ninja edit:

inf + inf = 2inf

2inf * 0 = 2.

But you could simply use my earlier statements and figure that much out on your own.

Theres no simplification.

You want to see inf + x = inf because you view inf as "the highest number" but when you do inf + 5 then inf + 5 = the highest number = inf.

But inf is not a number it's a concept, it's abstract, infinity.

To also answer your ninja edit:

inf + inf = 2inf

2inf * 0 = 2.

But you could simply use my earlier statements and figure that much out on your own.

Edited by Weird at 00:05 CST, 28 November 2014

Ok I see what you are doing. You basically just construct something like the hyper reals, re-label 0 as 0*, then add a new element 0 on which you define division. This doesn't count as division by zero unless you allow 1/0* which I believe you said wasn't allowed.

You want to see inf + x = inf because you view inf as "the highest number" but when you do inf + 5 then inf + 5 = the highest number = inf.I don't "want" anything. Stop incorrectly telling me what I think.

Edited by obi at 02:38 CST, 28 November 2014

Ofcourse you can't allow 1/0*.... Like I said I don't even want a symbol for 0* to be included in the lists of symbols.

You can't even write it down if you wanted to because you lack the symbol for it. (was my origional plan)

I only introduced the symbol last year to shut you and the other guy up because you couldn't believe that either, and it was hard to argue the point without being able to write it down ;).

And yes it's similar to the hyperreals but I don't need the rounding function (st(x)) to be so dominant because I simply keep the parts. Also the 'parts' actually can be brought back if you either multiply by inf or divide by 0.

So to answer your next question: 0 + 0 != 0 (you can't simply introduce 0's for free, which I explained last year as well) because 0 is an infinitessimal.

Like I said last year as well.... All I do here is alter some minor notational things such that from a philosophical point math makes better sense.

You can't even write it down if you wanted to because you lack the symbol for it. (was my origional plan)

I only introduced the symbol last year to shut you and the other guy up because you couldn't believe that either, and it was hard to argue the point without being able to write it down ;).

And yes it's similar to the hyperreals but I don't need the rounding function (st(x)) to be so dominant because I simply keep the parts. Also the 'parts' actually can be brought back if you either multiply by inf or divide by 0.

So to answer your next question: 0 + 0 != 0 (you can't simply introduce 0's for free, which I explained last year as well) because 0 is an infinitessimal.

Like I said last year as well.... All I do here is alter some minor notational things such that from a philosophical point math makes better sense.

So you can't divide by zero in your system, which is what started the whole thing...

So to answer your next question: 0 + 0 != 0 (you can't simply introduce 0's for free, which I explained last year as well) because 0 is an infinitessimal.All this talk about inf and 0 is a red herring. You have added a NEW element which you have labeled as 0, but which has none of the properties of 0 and then argued you can divide by zero. Now you are trying to make out your system does not have a zero element. So you can't divide by zero!

Edited by obi at 13:12 CST, 28 November 2014

Look here....

I've been pretty polite up till now and I'd like to keep it that way.

But it seems as if you're trying to put blame on me for your own incapability to able to use your brain.

I never altered my story.

That you fail to see the point is completely your own fault.

I can't deal with these nuclear bomb attacks of ignorance...........

I've been pretty polite up till now and I'd like to keep it that way.

But it seems as if you're trying to put blame on me for your own incapability to able to use your brain.

I never altered my story.

That you fail to see the point is completely your own fault.

I can't deal with these nuclear bomb attacks of ignorance...........

I've been pretty polite up till now and I'd like to keep it that way.Whats with the threat? Your actions are up to you, not me. I am being polite even though you have already started insulting me.

You said you could divide by zero. Then you went into this whole thing involving inf, 0 etc. When it was pointed out that your system doesn't have a zero element (because it's obviously not 0) you came up with 0*, which has the properties of a zero element. Then you said you can't divide by 0*. So you can't divide by zero.

If you say that you don't have a zero element (x-x= NOTHING LOL) then you can't divide by zero in your system, because it doesn't exist.

In between insults, maybe you could quote for me exactly what in the above you disagree with.

Edited by obi at 14:00 CST, 28 November 2014

I think you are just doing this to piss me off....

Nobody can be this ignorant.

I already explained this to you last year as well.

I think you are being very impolite. I told you several times already that I've answered all your idiotic questions, yet here you are again disagreeing with stuff. Enquireing further nonsense.

I don't disagree with you, you don't understand me and thus YOU disagree with me.

I can't make my point any clearer as it requires the reader to actually think about mathematics abstractly, something which you seem completely unable, or at the very least reluctant, to do.

The problem is your understanding of infinity. If you write down 0.9999.... and continue on writing 9's infinity many times then the resulting number = 1.

Just like 1 / 3 * 3 = 0.99999.... = 1.

To**explain that concept to you** I took the liberty to slightly alter notation such that 0 resembles a slightly different concept.

Such that we can say that 1 - 0 = 0.9999....

That you then wanted this to be fully consistent with current day math requires extra work but I did that last year (in hindsight this was a very bad decision by me as I am continuously being amazed by your whining and misunderstanding).

This 'fix' would require you to keep track of stuff such that:

1 - 0 = 0.9999...(9)

(1 - 0) - 0 = 0.9999...(8)

etc.

1 - (0 - 0) = 1

And you are simply allowed to do this if you so wish it doesn't break any result. The thing that it breaks is YOUR IDEA OF MATH. Not math itself.

Which I have now explained YET AGAIN (man I am nice I wasted yet another 5 minutes on your ignorance even though I think it's not my duty to educate you).

So will you now plz for once in your life sit down and think about the concept rather than whine out your own ignorance?

Nobody can be this ignorant.

I already explained this to you last year as well.

I think you are being very impolite. I told you several times already that I've answered all your idiotic questions, yet here you are again disagreeing with stuff. Enquireing further nonsense.

I don't disagree with you, you don't understand me and thus YOU disagree with me.

I can't make my point any clearer as it requires the reader to actually think about mathematics abstractly, something which you seem completely unable, or at the very least reluctant, to do.

The problem is your understanding of infinity. If you write down 0.9999.... and continue on writing 9's infinity many times then the resulting number = 1.

Just like 1 / 3 * 3 = 0.99999.... = 1.

To

Such that we can say that 1 - 0 = 0.9999....

That you then wanted this to be fully consistent with current day math requires extra work but I did that last year (in hindsight this was a very bad decision by me as I am continuously being amazed by your whining and misunderstanding).

This 'fix' would require you to keep track of stuff such that:

1 - 0 = 0.9999...(9)

(1 - 0) - 0 = 0.9999...(8)

etc.

1 - (0 - 0) = 1

And you are simply allowed to do this if you so wish it doesn't break any result. The thing that it breaks is YOUR IDEA OF MATH. Not math itself.

Which I have now explained YET AGAIN (man I am nice I wasted yet another 5 minutes on your ignorance even though I think it's not my duty to educate you).

So will you now plz for once in your life sit down and think about the concept rather than whine out your own ignorance?

By weltschmerz - Reply to #206

Things might become a little clearer if you mentioned that you're using two (rather unrelated) mathematical notions there. One being convergent sequences of numbers - the 0.999 thing - where some basic arithemtics is commutative with respect to taking the limit of the sequence instead of its elements. Like lim (a(n) + b(n)) = lim a(n) + lim b(n). And the other is the extended real number system and its arithmetic, as detailed e.g. here: http://en.wikipedia.org/wiki/Extended_real_nu...operations

Edited by weltschmerz at 11:26 CST, 29 November 2014

It all depends on how you view math.

There are 2 kinds of people who "ace math classes" those who remember concepts, names and patterns. And those who understand concepts and patterns.

Once you understand concepts math turns into "a playing field" where you can "play around" and "tinker with math".

Once you remember the concepts, names and patterns you get locked up in whatever view was taught to you, and you start to see math as "restricting", "strict/fixed", "true or false".

I fear that a LOT of people are caught in the strictness of math because of this.

There are 2 kinds of people who "ace math classes" those who remember concepts, names and patterns. And those who understand concepts and patterns.

Once you understand concepts math turns into "a playing field" where you can "play around" and "tinker with math".

Once you remember the concepts, names and patterns you get locked up in whatever view was taught to you, and you start to see math as "restricting", "strict/fixed", "true or false".

I fear that a LOT of people are caught in the strictness of math because of this.

By weltschmerz - Reply to #208

Well, regarding the tinkering there's one basic rule you may want to adhere to: whatever you do, it shouldn't lead to obvious or nonobvious contradictions. Because at that point people won't accept it as math anymore.

And since the proof of contradiction-freeness often isn't that easy to accomplish I took the liberty of linking to the extended real numbers article. The infinity/division by zero stuff has been pretty well studied a while ago already, including what one may meaningfully do with those concepts without running into fallacies, so basing your argument on that already accomplished work might possibly make life a little easier.

And since the proof of contradiction-freeness often isn't that easy to accomplish I took the liberty of linking to the extended real numbers article. The infinity/division by zero stuff has been pretty well studied a while ago already, including what one may meaningfully do with those concepts without running into fallacies, so basing your argument on that already accomplished work might possibly make life a little easier.

By weltschmerz - Reply to #210

Supremely easy!

Let me still give a warning though about taking limits (1) for their sequences (0.9999...). You're sometimes getting the most unexpected results specifically when divergent sequences are involved (which sometimes you even not easily recognize as such).

Trivial example: consider the sequence of sums of 1

1 2 3 4 5 ...

which diverges to inf, and the negative

-1 -2 -3 -4 ...

which diverges to -inf. But the sum of those sequences

0 0 0 0 ...

converges to 0. Now, if I could take the limit for the sequence that would mean

inf - inf = 0

which, by associativity of addition, would for example imply that

1 = 0

because inf + 1 = inf. Not exactly what one would normally expect.

Let me still give a warning though about taking limits (1) for their sequences (0.9999...). You're sometimes getting the most unexpected results specifically when divergent sequences are involved (which sometimes you even not easily recognize as such).

Trivial example: consider the sequence of sums of 1

1 2 3 4 5 ...

which diverges to inf, and the negative

-1 -2 -3 -4 ...

which diverges to -inf. But the sum of those sequences

0 0 0 0 ...

converges to 0. Now, if I could take the limit for the sequence that would mean

inf - inf = 0

which, by associativity of addition, would for example imply that

1 = 0

because inf + 1 = inf. Not exactly what one would normally expect.

By weltschmerz - Reply to #222

Don't know. What about this school http://www.mathi.uni-heidelberg.de/?lang=en ?

By weltschmerz - Reply to #226

Mess with him because he seemed to take a little interest in my upbringing? Don't intend to.

By weltschmerz - Reply to #235

Thanks. But I was really just involving myself for a cautionary word about sequence arithmetic. Namely, that it really just works in the expected way when all involved series are convergent. Like detailed here:

http://en.wikipedia.org/wiki/Convergent_sequence#Properties

But since some of this discussion was about infinity, in which case divergent sequences may become a subject of interest, I thought it wouldn"t do any harm to remind everybody that those behave wildly different.

http://en.wikipedia.org/wiki/Convergent_sequence#Properties

But since some of this discussion was about infinity, in which case divergent sequences may become a subject of interest, I thought it wouldn"t do any harm to remind everybody that those behave wildly different.

By weltschmerz - Reply to #236

No they didn't. Maybe read again for another go at what the point was.

And frankly, 0.999.. isn't 1. The limit is 1. And 0.999... is only as good as 1 within any given margin of error. Mind the difference.

And frankly, 0.999.. isn't 1. The limit is 1. And 0.999... is only as good as 1 within any given margin of error. Mind the difference.

you mean that if you "use my notation and throw it into regular notated math" that it doesn't work out or something like that?

Your point seems not clear to me. Perhaps you're talking about different systems?

Also if 0.999... means that the 9's continue on till infinity, then it is 1.

You don't have to hold any margin.

This is easiest shown with writing down 1/3 + 1/3 + 1/3 = 3*1/3 = 3 / 3 = 1

(1/3 = 0.333333....

3x 0.33333.... = 0.99999....)

This is not a "limit" question, it's a notation thing.

Your point seems not clear to me. Perhaps you're talking about different systems?

Also if 0.999... means that the 9's continue on till infinity, then it is 1.

You don't have to hold any margin.

This is easiest shown with writing down 1/3 + 1/3 + 1/3 = 3*1/3 = 3 / 3 = 1

(1/3 = 0.333333....

3x 0.33333.... = 0.99999....)

This is not a "limit" question, it's a notation thing.

Edited by Weird at 15:34 CST, 29 November 2014

By weltschmerz - Reply to #240

There is no "continue on till infinity" in mathematical analysis, because you can't perform any "continuing on till infinity". You would grow a pretty long beard when trying to prove anything by "continuing on till infinity", wouldn't you.

That's why limits and infinitesimal calculus were invented. To account for that tiny bit you never can really act on, and then show that this tiny bit doesn't really matter under a good deal of circumstances.

That doesn't make the tiny bit just entirely vanish though. The series of the sum of 9 divided by powers of 10 isn't equal 1. It merely converges towards 1. Not more.

That's why limits and infinitesimal calculus were invented. To account for that tiny bit you never can really act on, and then show that this tiny bit doesn't really matter under a good deal of circumstances.

That doesn't make the tiny bit just entirely vanish though. The series of the sum of 9 divided by powers of 10 isn't equal 1. It merely converges towards 1. Not more.

By weltschmerz - Reply to #242

That isn't really productive input I'm afraid. In contrast to very peculiar situations, like when about to have an orgasm, for most practical purposes "being arbitrarily close" is indeed good enough.

Its productive if you care about being correct. Saying they are "close enough" implies they are different numbers. They are not; 0.999... is another way of writing 1.

Edited by obi at 18:16 CST, 29 November 2014

By weltschmerz - Reply to #246

You may define it that way if you want to. If 10^n denotes 10 taken to the power of n, you may define 1 as the limit of the series of sums of 9/10^n. And while that's not how it's done in modern analysis, where 1 is defined as the neutral element of multiplication within the field of real numbers, it's still a legitimate definition. The one point worth paying attention to being that there's still a difference between the series and its limit.

By weltschmerz - Reply to #249

You'd have to say what 0.99.. is supposed to denote in that definition. For starters, which equivalence class of Cauchy sequences precisely would it represent?

By weltschmerz - Reply to #252

Precisely. A limit.

By weltschmerz - Reply to #255

Again, you'd have to say what "0.99.." is supposed to mean. The natural assumption would be that it denotes the series 9/10^1 + 9/10^2 + 9/10^3 and so on. As such, that's not a number but a series, though a convergent one with 1 as the limit it's arbitrarily coming close - converging - to. But it's still not a number, it's a series with a limit, and there's a clear distinction between those two. And what the Wikipedia article does is pretty much mixing those two up notationally.

By weltschmerz - Reply to #257

No, that's what I said. Any halfway normal mathematician would read "0.99..." as the series, not as its limit. It"s entirely trivial, a banality to the max, that the limit is 1. So nobody in his sane mind would ever use "0.99..." to denote 1, he would write just 1. He might write "0.99..." only if he wanted to denote the series converging 1.

As such, this whole 0.999... thing amounts to little more than deliberate confusion. People make it look like they were talking about the series. But then they pull the limit of the series out of their asses like "hey that's what I really meant with 0.99...".

As such, this whole 0.999... thing amounts to little more than deliberate confusion. People make it look like they were talking about the series. But then they pull the limit of the series out of their asses like "hey that's what I really meant with 0.99...".

By weltschmerz - Reply to #259

Try writing it down and you have your answer. See you then.

Edited by obi at 20:32 CST, 29 November 2014

By weltschmerz - Reply to #261

You may safely skip those zeros because they don't add anything, in contrast to 9s divided by powers of 10. Otherwise you're right, you can't write down pi. Nobody can and nobody ever will.

By weltschmerz - Reply to #263

The point wasn't if we're able to write down a number, because 1 is easy enough to write down anyway, isn't it.

By weltschmerz - Reply to #266

Did I? Where?

right between

"But it's still not a number, it's a series with a limit, and there's a clear distinction between those two. And what the Wikipedia article does is pretty much mixing those two up notationally."

And

"The point wasn't if we're able to write down a number, because 1 is easy enough to write down anyway, isn't it."

Kinda around the

"Right, so whether or not we can write out a number in full has nothing to do with whether it is a valid number or not. So is there any number which has a decimal expansion 0.99."

mark where you lose it.

"But it's still not a number, it's a series with a limit, and there's a clear distinction between those two. And what the Wikipedia article does is pretty much mixing those two up notationally."

And

"The point wasn't if we're able to write down a number, because 1 is easy enough to write down anyway, isn't it."

Kinda around the

"Right, so whether or not we can write out a number in full has nothing to do with whether it is a valid number or not. So is there any number which has a decimal expansion 0.99."

mark where you lose it.

By weltschmerz - Reply to #275

Couldn't quite follow but if your "logic" makes you feel better, why not.

how can you not follow that?

First you say that 0.999... is an infinite series with a limit. Then Obi points out that all numbers can be written as infinite series. After which you say that it's not the point if it's a valid number or not because 1 is easy enough to write.

Which is not an actual argument against 0.999... not being a number.

If you want to argue that 0.9999.... is not 1 then you're kinda gonna be forced to use infinitesimals in some sort or another. Which I've been saying.

If you say that 0.999.. = 1 then you've proven yourself wrong as well because obviously 1 is a number and thus if they are equal than 0.999.. must also be a number (namely the same).

The last option (the one you're gonna go for) is to say that a "Limit is something different" and that we don't understand how a liimt works.

Meanwhile it is the limit from 1 -> infinity.... At which point you are still dependant upon how you go about with infinity. And there is still a very good point to say that 1 = 0.999... (Because it is Cauchy)

First you say that 0.999... is an infinite series with a limit. Then Obi points out that all numbers can be written as infinite series. After which you say that it's not the point if it's a valid number or not because 1 is easy enough to write.

Which is not an actual argument against 0.999... not being a number.

If you want to argue that 0.9999.... is not 1 then you're kinda gonna be forced to use infinitesimals in some sort or another. Which I've been saying.

If you say that 0.999.. = 1 then you've proven yourself wrong as well because obviously 1 is a number and thus if they are equal than 0.999.. must also be a number (namely the same).

The last option (the one you're gonna go for) is to say that a "Limit is something different" and that we don't understand how a liimt works.

Meanwhile it is the limit from 1 -> infinity.... At which point you are still dependant upon how you go about with infinity. And there is still a very good point to say that 1 = 0.999... (Because it is Cauchy)

Edited by Weird at 22:55 CST, 29 November 2014

By weltschmerz - Reply to #282

No, obi didn't point out that all numbers can be written as infinite series, which would be a trivial observation. He observed that many numbers only representable as infinite series can't be written down at all, amongst them the series 0.99..

And so on.

This is becoming pretty retarded now.

And so on.

This is becoming pretty retarded now.

By weltschmerz - Reply to #288

0.99.. isn't a decimal representation of a number I'm afraid. You'd have to exactly specify, in mathematical notation, what those dots at the end are supposed to mean.

By weltschmerz - Reply to #327

It's a sum of integrals multiplied with powers of ten. And a sum is, by definition, finite. Otherwise it's called a series.

By weltschmerz - Reply to #370

With finite I obviously meant the number of summands. So when that number isn't finite it's called a series. Which isn't a number but a set, a so called "sequence", of numbers. And if that series converges you may then indeed chose a number, it's so called limit, to represent that series for various kinds of calculations. There's still a huge difference between a set of numbers and a number though, and if math didn't make that distinction it really wouldn't be of much use.

I guess it is a matter of definition. You can define the decimals such that expression like 0.99... are not valid, then every real will have a unique decimal expression. You can also define them as the limit of their partial sums, in which case 0.99... is valid and equal to 1. I would assume when people argue about 0.99...=1 they are using the second definition.

By weltschmerz - Reply to #423

Sure. You can define dumbass to be weird and then dumbass=weird.

The point is if a notation and according definitions make sense. In this case the opposite holds true, it's misleading and inducing all the wrong ideas. You're seeing the detrimental effects right here on this board.

You know, that's what a good deal of math actually is about, too. Choosing the right notation that adequately expresses the core features of the topic at hand, in particular to give the reader the right ideas.

The point is if a notation and according definitions make sense. In this case the opposite holds true, it's misleading and inducing all the wrong ideas. You're seeing the detrimental effects right here on this board.

You know, that's what a good deal of math actually is about, too. Choosing the right notation that adequately expresses the core features of the topic at hand, in particular to give the reader the right ideas.

By asdfasdfasdf - Reply to #424

which is a good reason why people with advanced intuitive understanding of mathematics have to invent notations that others have difficulty grasping and argue against because they don't fit into their safely molded order of things as they have been and always should be.

I have no problem with people defining anything they want. What is annoying is when they

(a) won't clearly define what they mean

(b) get angry when you ask them question to try and figure out what they mean

(c) reuse existing notation for different things without telling you, then get angry when you justifiably get confused

(a) won't clearly define what they mean

(b) get angry when you ask them question to try and figure out what they mean

(c) reuse existing notation for different things without telling you, then get angry when you justifiably get confused

By asdfasdfasdf - Reply to #430

don't bother speaking to me, idiot. the only redeeming quality of your character is your ignorance, and then only because it serves so well as a warning for any person of philosophical integrity to avoid your brainless dumbfuckery, moron.

Edited by obi at 17:50 CST, 1 December 2014

By asdfasdfasdf - Reply to #434

somehow it's sadder when there are two of them

Listen here you dimwitted little cunt. For over 2 posts I've done my best to remain civil in the face of your incessant, misguided bullshit but now you have forced my hand. Why don't you try reading a fucking shallow Wikipedia page instead of crying at me to wipe your intellectual asshole for you, kid.

edit: bitch

edit: bitch

Edited by obi at 23:35 CST, 1 December 2014

By asdfasdfasdf - Reply to #430

ps fuck you

No you can't....

Weird is already defined:

weird

wird/

adjective

adjective: weird; comparative adjective: weirder; superlative adjective: weirdest

1.

suggesting something supernatural; uncanny.

"the weird crying of a seal"

synonyms: uncanny, eerie, unnatural, supernatural, unearthly, otherworldly, ghostly, mysterious, strange, abnormal, unusual;

eldritch;

informalcreepy, spooky, freaky

"weird apparitions"

antonyms: normal

informal

very strange; bizarre.

"a weird coincidence"

synonyms: bizarre, quirky, outlandish, eccentric, unconventional, unorthodox, idiosyncratic, surreal, crazy, peculiar, odd, strange, queer, freakish, zany, madcap, outré; More

informalbizarro, wacky, freaky, way-out, offbeat, off the wall, wacko

"a weird sense of humor"

antonyms: conventional

archaic

connected with fate.

noun

Scottisharchaic

noun: weird; plural noun: weirds

1.

a person's destiny.

verb

North Americaninformal

verb: weird; 3rd person present: weirds; past tense: weirded; past participle: weirded; gerund or present participle: weirding

1.

induce a sense of disbelief or alienation in someone.

Weird is already defined:

weird

wird/

adjective

adjective: weird; comparative adjective: weirder; superlative adjective: weirdest

1.

suggesting something supernatural; uncanny.

"the weird crying of a seal"

synonyms: uncanny, eerie, unnatural, supernatural, unearthly, otherworldly, ghostly, mysterious, strange, abnormal, unusual;

eldritch;

informalcreepy, spooky, freaky

"weird apparitions"

antonyms: normal

informal

very strange; bizarre.

"a weird coincidence"

synonyms: bizarre, quirky, outlandish, eccentric, unconventional, unorthodox, idiosyncratic, surreal, crazy, peculiar, odd, strange, queer, freakish, zany, madcap, outré; More

informalbizarro, wacky, freaky, way-out, offbeat, off the wall, wacko

"a weird sense of humor"

antonyms: conventional

archaic

connected with fate.

noun

Scottisharchaic

noun: weird; plural noun: weirds

1.

a person's destiny.

verb

North Americaninformal

verb: weird; 3rd person present: weirds; past tense: weirded; past participle: weirded; gerund or present participle: weirding

1.

induce a sense of disbelief or alienation in someone.

By weltschmerz - Reply to #440

Only meant to give an example of how little helpful the wrong notation can be, and how it might be inducing all the wrong ideas. So I'm certainly d'accord with you giving the point additional emphasis and highlighting.

"There is no "continue on till infinity" in mathematical analysis"

Wikipedia 1st line:

"Mathematical analysis is a branch of mathematics that includes the theories of differentiation, integration, measure, limits,**infinite series**, and analytic functions"

You are right that "to deal with this infinity" limits and infinitesimals were invented.

However your last lines don't make sense:

"The series of the sum of 9 divided by powers of 10 isn't equal 1. It merely converges towards 1."

Because the infinite series of the sum of 9 divided by powers of 10 == 1.

Not because it converges there but because it is equal.

http://en.wikipedia.org/wiki/0.999...

What you're describing is how current mathematics deals with the concepts. But you don't think about what these concepts truelly are.

Thinking about this is what mathematicians should imo (also) do. As Euler used to do (who I find amazing :D).

Wikipedia 1st line:

"Mathematical analysis is a branch of mathematics that includes the theories of differentiation, integration, measure, limits,

You are right that "to deal with this infinity" limits and infinitesimals were invented.

However your last lines don't make sense:

"The series of the sum of 9 divided by powers of 10 isn't equal 1. It merely converges towards 1."

Because the infinite series of the sum of 9 divided by powers of 10 == 1.

Not because it converges there but because it is equal.

http://en.wikipedia.org/wiki/0.999...

What you're describing is how current mathematics deals with the concepts. But you don't think about what these concepts truelly are.

Thinking about this is what mathematicians should imo (also) do. As Euler used to do (who I find amazing :D).

By weltschmerz - Reply to #251

Mathematical analysis dealing with infinite series doesn't imply any "continuing to infinity". Quite the contrary, it's mostly about showing that we don't need to - seeing how we wouldn't be able to anyway - given we are willing to accept an amount of imprecision that can be arbitrarily contained. The imprecision for example that's implied in those dots there in "0.9...", which factually isn't even a number.

And regarding the 0.999 Wikipedia article, you might want to consider paying some attention to a definition it's linking to in the Cauchy sequence section, namely the definition of a limit

http://en.wikipedia.org/wiki/Limit_of_a_seque...Definition

And regarding the 0.999 Wikipedia article, you might want to consider paying some attention to a definition it's linking to in the Cauchy sequence section, namely the definition of a limit

http://en.wikipedia.org/wiki/Limit_of_a_seque...Definition

I wonder if at any place rather than claiming that you disagree with me, you actually will disagree with me.

Because you're not disagreeing with anything other than my choice of words.

The only cause for this disagreement is because I deal with the concept of infinity while you deal with your mathematical construct of infinity (the one you learned, while there are other views on this which lead to (for instance) infinitesimals).

You're one of the guys who thinks that math originates in a book and refuse to think about the philosophical concepts and problems as such.

You really should try to think about the core issues of math from a philosophical point and then reason through how you can construct an exact solution for these issues.

Actually it wouldn't suprise me in the least if you are fau from the other thread. He was arguing from the exact same lack of imagination and saying that I therefor was wrong.

Imo you don't understand math, you "do math". You don't "think mathematically" but you "apply math to problems".

In this regard you are equal to obi.

And it kinda saddens me that the both of you haven't had a chance to actually learn what math is about.

Because you're not disagreeing with anything other than my choice of words.

The only cause for this disagreement is because I deal with the concept of infinity while you deal with your mathematical construct of infinity (the one you learned, while there are other views on this which lead to (for instance) infinitesimals).

You're one of the guys who thinks that math originates in a book and refuse to think about the philosophical concepts and problems as such.

You really should try to think about the core issues of math from a philosophical point and then reason through how you can construct an exact solution for these issues.

Actually it wouldn't suprise me in the least if you are fau from the other thread. He was arguing from the exact same lack of imagination and saying that I therefor was wrong.

Imo you don't understand math, you "do math". You don't "think mathematically" but you "apply math to problems".

In this regard you are equal to obi.

And it kinda saddens me that the both of you haven't had a chance to actually learn what math is about.

Edited by Weird at 21:10 CST, 29 November 2014

By weltschmerz - Reply to #265

Do you really mean to suggest that the "0.99.. series vs. its 1 limit" debate was touching any of the philosophical core issues of mathematics?

Yes it does.

The question on how to deal with infinitely small differences (and thus with the concept of infinity).

That you don't see this as a philosophical point kinda baffles me.... Because it's the ONLY thing that I argued.

That you didn't get that after 20 posts of me telling you that you don't get it... Kinda shows my point doesn't it?

Also I'm kinda amazed that you would say that infinity is not a philosophical core issue of mathematics.

The question on how to deal with infinitely small differences (and thus with the concept of infinity).

That you don't see this as a philosophical point kinda baffles me.... Because it's the ONLY thing that I argued.

That you didn't get that after 20 posts of me telling you that you don't get it... Kinda shows my point doesn't it?

Also I'm kinda amazed that you would say that infinity is not a philosophical core issue of mathematics.

By weltschmerz - Reply to #272

How to deal with infinitely small differences? No clue what that's supposed to mean.

Mathematical analysis deals with differences that can be assumed to be made arbitrarily - not infinitely - small. And then shows how in many situations those may be neglected. That's all there's to it.

I mean seriously, do really think a computer, with its limited precision math, would depend on deep mathematical philosophy to draw a circle?

Mathematical analysis deals with differences that can be assumed to be made arbitrarily - not infinitely - small. And then shows how in many situations those may be neglected. That's all there's to it.

I mean seriously, do really think a computer, with its limited precision math, would depend on deep mathematical philosophy to draw a circle?

"How to deal with infinitely small differences? No clue what that's supposed to mean." <-- perhaps that's your problem... why you don't understand what I was trying to say.

"Mathematical analysis deals with...." <-- I wasn't talking about analysis anywhere. I was talking about the entirety of math the concepts behind it.

The 'difference between reals and hypperreals' (if you want to call it like that) where which one deals with infinity and what the differences are. And how to introduce a fun way of thinking with an intuitive way of notation. While not breaking anything in between.

I know exactly how a computer draws a circle....

I don't argue anything related to that?

"Mathematical analysis deals with...." <-- I wasn't talking about analysis anywhere. I was talking about the entirety of math the concepts behind it.

The 'difference between reals and hypperreals' (if you want to call it like that) where which one deals with infinity and what the differences are. And how to introduce a fun way of thinking with an intuitive way of notation. While not breaking anything in between.

I know exactly how a computer draws a circle....

I don't argue anything related to that?

By weltschmerz - Reply to #281

You were talking about the entirety of math concepts? Dear me.

Do you only remotely realize how many different fields mathematics consists of? And how each of them have their entirely different set of axioms they start from? Like mathematical logic, analysis, algebra, topology? And how your beloved infinity "philosophical" problem is just the tiniest amongst the tiniest of "issues" hardly anybody is concerned with these days, because approximation works so well for all practical purposes, including landing spacecraft on tiny pieces of matter rocketing through space?

Good lord, man. Get a grip.

Do you only remotely realize how many different fields mathematics consists of? And how each of them have their entirely different set of axioms they start from? Like mathematical logic, analysis, algebra, topology? And how your beloved infinity "philosophical" problem is just the tiniest amongst the tiniest of "issues" hardly anybody is concerned with these days, because approximation works so well for all practical purposes, including landing spacecraft on tiny pieces of matter rocketing through space?

Good lord, man. Get a grip.

Edited by weltschmerz at 22:58 CST, 29 November 2014

Why do you continuously point to "purposes of math" (and or quality of physics)?

Mathematics is not "applying math" I've said this multiple times before.

Also I didn't say that infinity was a major issue in math. But it is the issue at hand here.

As obi was confused as to why 0.999... = 1. The same thing that you seem to be pretty confused about tbh.

And the reason for this lies in how you view infinity.

I tried to explain this through a somewhat funny notation using a concept like infinitesimals. But altering the notation a bit so that it makes more sense. Using the symbol 0 as a basic infinitesimal unit.

And altering the 0 and infinity slightly such that they function more similar to an imaginairy part of a complex number.

But seeing how you never ever tried to think about this.... I guess that you're not interrested in anything other than continuously claiming how awesome you are at math and how many terms you know (woooooot!)

Mathematics is not "applying math" I've said this multiple times before.

Also I didn't say that infinity was a major issue in math. But it is the issue at hand here.

As obi was confused as to why 0.999... = 1. The same thing that you seem to be pretty confused about tbh.

And the reason for this lies in how you view infinity.

I tried to explain this through a somewhat funny notation using a concept like infinitesimals. But altering the notation a bit so that it makes more sense. Using the symbol 0 as a basic infinitesimal unit.

And altering the 0 and infinity slightly such that they function more similar to an imaginairy part of a complex number.

But seeing how you never ever tried to think about this.... I guess that you're not interrested in anything other than continuously claiming how awesome you are at math and how many terms you know (woooooot!)

By weltschmerz - Reply to #286

Hahaha, you make me laugh dude. You're throwing trivialities around in intentionally confusing notation, to make it look as if you were talking about something worthwhile, while it's in fact the dumbest banalities to be found in mathematical analysis.

Like the 0.99.. series converging towards 1, where you then pretend that it was equal 1 if you "continued til infinity". Jesus, what a joke. Well, "continue til infinity". Prove it your claims true. And good luck with that. Clown.

Like the 0.99.. series converging towards 1, where you then pretend that it was equal 1 if you "continued til infinity". Jesus, what a joke. Well, "continue til infinity". Prove it your claims true. And good luck with that. Clown.

finaly you seem to be starting to understand why I got tired of explaining these things and started calling you stupid.

Yes they are trivial and banal... yet you and don't understand them.

Not my fault.

I don't think that my notation is in any way confusing though.

I explained the concept (which you wouldn't attempt to understand yet it was extremely simple) and explained the notation. Nothing special going on there.

I have already proven the claim that it's equal with the 1/3 * 3 example.

1/3 = 0.333....

3 * 0.333... = 0.999...

3 * 1 / 3 = 1

Tada there is a direct mathematical equality there.

That you have a degree in mathematics.... What a joke. Clown.

Yes they are trivial and banal... yet you and don't understand them.

Not my fault.

I don't think that my notation is in any way confusing though.

I explained the concept (which you wouldn't attempt to understand yet it was extremely simple) and explained the notation. Nothing special going on there.

I have already proven the claim that it's equal with the 1/3 * 3 example.

1/3 = 0.333....

3 * 0.333... = 0.999...

3 * 1 / 3 = 1

Tada there is a direct mathematical equality there.

That you have a degree in mathematics.... What a joke. Clown.

Edited by Weird at 10:23 CST, 30 November 2014

By weltschmerz - Reply to #300

There is no equality because you haven't defined what "..." is supposed to mean, notwithstanding your "continue til infinity" nonsense which isn't within the realm of mathematical rigor. I mean, that's one of the major achievements mathematics has us provided with, that we don't need to "continue til infinity" to attain some results we can work with. Because it would take a pretty long time doing that, a basic realization you already seem to have tremendous trouble comprehending.

By weltschmerz - Reply to #304

Repeating how often? If you mean infinity, that's not something you can meaningfully calculate with. It'd be like saying "if you repeatedly divide 1 by 10 infinitely you'll finally arrive at 0". Except you never get there. Really that hard?

Why do you ask me?

Is it not much better to hide your ignorance on your 'expert area' (as you claim that you know everything better than me) by actually trying to find the answer by looking in your textbook or searching the internet?

It is a perfectly normal, very intuitive, notation within math.

Is it not much better to hide your ignorance on your 'expert area' (as you claim that you know everything better than me) by actually trying to find the answer by looking in your textbook or searching the internet?

It is a perfectly normal, very intuitive, notation within math.

By weltschmerz - Reply to #311

Still more rubbish. It's, at best, an outlandish notation nobody interested in proper communication of the underlying concepts would ever use. Specifically because it's misleading, as it suggests that you could construct a number starting with 0.9 which would be equal to one. Which you can't, because whatever you can do has to be done in a finite number of steps. And beyond that, you can only make estimates about how close you can get with so many more steps, which are again finite even if arbitrarily many.

Maybe you should make an attempt at understanding what you're mindlessly copy-and-pasting around. Mr. "continue til infinity" jokester.

Maybe you should make an attempt at understanding what you're mindlessly copy-and-pasting around. Mr. "continue til infinity" jokester.

maybe you should learn math rather than blurting out this crap that numbers have to be written down in a finite number of steps.

Your understanding of mathematical concepts is obviously filled with a LOT of mistakes.

And you've shown so several times... It is not my job to do your professors job. So unless you start paying me I won't continue to point out how retarded you are.

Your understanding of mathematical concepts is obviously filled with a LOT of mistakes.

And you've shown so several times... It is not my job to do your professors job. So unless you start paying me I won't continue to point out how retarded you are.

By weltschmerz - Reply to #319

Here clown an exercise, Zeno's Achilles & the tortoise "paradox", to make an attempt at least at getting you on track

http://en.wikipedia.org/wiki/Zeno%27s_paradox...e_tortoise

If you can't figure it out yourself just read through "the paradoxes in modern times" section, to get a vague idea about where the problem specifically with "continuing til infinity" lies.

I mean, looking back, it's really kind of tragic. How you're blabbering about "infinitesimals" and such, and when a notional gimmick of extraordinary stupidity makes those "infinitesimals" vanish entirely you're completely content with such rubbish without seeing any problem. Dear me.

http://en.wikipedia.org/wiki/Zeno%27s_paradox...e_tortoise

If you can't figure it out yourself just read through "the paradoxes in modern times" section, to get a vague idea about where the problem specifically with "continuing til infinity" lies.

I mean, looking back, it's really kind of tragic. How you're blabbering about "infinitesimals" and such, and when a notional gimmick of extraordinary stupidity makes those "infinitesimals" vanish entirely you're completely content with such rubbish without seeing any problem. Dear me.

By weltschmerz - Reply to #322

So, to conclude, be informed that mathematics never tries to prove anything by "continuing til infinity". Because it's impossible to do that. If you're trying to prove for example that some statement S holds true for all natural numbers n you're not doing it by "continuing til infinity". You prove it by proving it for 0 and then prove that, if S holds for n, it also holds for n+1. That"s it. You're proving something for an infinite set of numbers with a finite set of steps.

So, regarding decimal representations of numbers, they're obviously equivalent to finite tuples of natural number coefficients to reciprocal powers of ten. Like 0.999 is equal to 9*1/10^1 + 9*1/10^2 + 9*1/10^3 and thus equivalent to the tuple (9,9,9).

But then, what's 0.99... supposed to mean anyway? Something like 9*1/10^1 + 9*1/10^2 + .. and then continue adding "til infinity"? That doesn't make any sense, because you can't do that.

What it really means is a series of numbers

0.9

0.99

0.999

0.9999

which basically amounts to a function f of the natural numbers N into R. Like f(1)=0.9, f(2)=0.99 and f(n)=0.99..9 with n 9s. And mind the 9 at the end after the dots, for each n the decimal representation is finite.

And now, having a well formed representation of the situation under discussion, you may show that, given any miniscule interval around 1, you can find a (finite) n so that the value of n under this function and of every natural number larger than n is within this interval. Do you see how this explicitly does not involve any "continuing til infinity"? You just prove that the series, eventually, will come as close as you want with all its remaining members. That is, mathematics specifically works around infinity here by replacing "all" with "any given". While, at the same time, the series never - repeat: never - really becomes 1 at the same time.

And that's what mathematics now does: since we end up getting arbitrarily close anyway we may as well take the limit of the series for the series. While at the same time, and that's paramount, not mixing up those two.

And that's why a whole theory, like about the continuity of functions, ensues. Because now, that mathematics has introduced this arbitrarily miniscule imprecision, it has to painstakingly show under which operations its ok to maintain it by specifically proving that the imprecision continues to be arbitrarily miniscule under those operations and wouldn't suddenly get out of control. That's really what a very large part of mathematical analysis is concerned with.

In particular, writing something like 0.99... = 1 totally blurs the whole amount of care that generations of mathematicians had to learn understanding the hard way needs to be taken. The equal sign alone there is an atrocity, not to mention the 0.99.. notation inviting people to confuse the series with the limit. Still, if you really feel like "continuing til infinity" would be the way to go for you I won't be the one trying to interfere. Good luck.

So, regarding decimal representations of numbers, they're obviously equivalent to finite tuples of natural number coefficients to reciprocal powers of ten. Like 0.999 is equal to 9*1/10^1 + 9*1/10^2 + 9*1/10^3 and thus equivalent to the tuple (9,9,9).

But then, what's 0.99... supposed to mean anyway? Something like 9*1/10^1 + 9*1/10^2 + .. and then continue adding "til infinity"? That doesn't make any sense, because you can't do that.

What it really means is a series of numbers

0.9

0.99

0.999

0.9999

which basically amounts to a function f of the natural numbers N into R. Like f(1)=0.9, f(2)=0.99 and f(n)=0.99..9 with n 9s. And mind the 9 at the end after the dots, for each n the decimal representation is finite.

And now, having a well formed representation of the situation under discussion, you may show that, given any miniscule interval around 1, you can find a (finite) n so that the value of n under this function and of every natural number larger than n is within this interval. Do you see how this explicitly does not involve any "continuing til infinity"? You just prove that the series, eventually, will come as close as you want with all its remaining members. That is, mathematics specifically works around infinity here by replacing "all" with "any given". While, at the same time, the series never - repeat: never - really becomes 1 at the same time.

And that's what mathematics now does: since we end up getting arbitrarily close anyway we may as well take the limit of the series for the series. While at the same time, and that's paramount, not mixing up those two.

And that's why a whole theory, like about the continuity of functions, ensues. Because now, that mathematics has introduced this arbitrarily miniscule imprecision, it has to painstakingly show under which operations its ok to maintain it by specifically proving that the imprecision continues to be arbitrarily miniscule under those operations and wouldn't suddenly get out of control. That's really what a very large part of mathematical analysis is concerned with.

In particular, writing something like 0.99... = 1 totally blurs the whole amount of care that generations of mathematicians had to learn understanding the hard way needs to be taken. The equal sign alone there is an atrocity, not to mention the 0.99.. notation inviting people to confuse the series with the limit. Still, if you really feel like "continuing til infinity" would be the way to go for you I won't be the one trying to interfere. Good luck.

I don't get that Achilles tortoise thing?

If X is faster than Y then X will eventually ourtun Y, there's no infinite thing here?

Like take a real life example, granny goes to the store at 8am and she forgot her meds, you find that out few min later when she's 100 feet away from you, don't tell me you're stuck in a paradox of infinity and can't catch her?

If X is faster than Y then X will eventually ourtun Y, there's no infinite thing here?

Like take a real life example, granny goes to the store at 8am and she forgot her meds, you find that out few min later when she's 100 feet away from you, don't tell me you're stuck in a paradox of infinity and can't catch her?

to understand the paradox you shouldn't look at the problem in time but rather in epochs.

Where each epoch is Achilles catching up to where the tortoise was in the previous one.

There are ofcourse infinitely many of these epochs. (because everytime that he catches up the tortoise will have moved, and thus there will be a next epoch... That this distance gets smaller in each epoch doesn't matter. What matters is that there are infinitely many.

As each epoch is "at a further place in time" (and there are infinitely many) the paradox claims that you can thus never catch up.

Weltschmerz probably has a ton of issues with my explanation but I tried to leave out the math and simply explain the paradox in a bit more detail.

Where each epoch is Achilles catching up to where the tortoise was in the previous one.

There are ofcourse infinitely many of these epochs. (because everytime that he catches up the tortoise will have moved, and thus there will be a next epoch... That this distance gets smaller in each epoch doesn't matter. What matters is that there are infinitely many.

As each epoch is "at a further place in time" (and there are infinitely many) the paradox claims that you can thus never catch up.

Weltschmerz probably has a ton of issues with my explanation but I tried to leave out the math and simply explain the paradox in a bit more detail.

Edited by Weird at 06:53 CST, 1 December 2014

By weltschmerz - Reply to #338

At the core of the paradoxon is a misconception, namely that you could do something infinitely in a limited amount of time. Like taking a measurement of where Achilles currently stands. Or writing down a digit for a decimal number. In the paradox for example, there's a measurement taken each 1/2^n time interval, with n increasing towards infinity and the interval towards 0. That's impossible.

And because that's impossible, math has invented the infinitesimal, which basically is an approximation, because in reality one doesn't really need to keep looking infinitely if one is willing to accept an error that can be made arbitrarily small. And at that point the math starts working again, and only then. When you stop trying "continuing til infinity", as the residential jokester here thinks was possible.

And because that's impossible, math has invented the infinitesimal, which basically is an approximation, because in reality one doesn't really need to keep looking infinitely if one is willing to accept an error that can be made arbitrarily small. And at that point the math starts working again, and only then. When you stop trying "continuing til infinity", as the residential jokester here thinks was possible.

Ah so this paradox only works if there is no starting or ending destination, like house -> store in my story, but rather a granny in endless space always behind that one step ahead, even though the distance between us keeps getting smaller? (kinda like the .9999s in the paradox you're currently trying to debunk?)

By weltschmerz - Reply to #363

Maybe look at it this way.

You and your granny do that footrace and it's already clear that you're going to overturn her in 10 seconds. And at the sideline is that guy looking where you currently are.

As the paradox now devises it, he's going to look faster and faster where you currently are, while you're in the process of catching up. In fact, the speed at which he's looking faster makes it impossible for him to ever finish looking until you have reached your granny. At that point, he's kind of trapped in his own timeline and will never experience the moment when you and your granny meet. Which of course is impossible, so that's basically the mind trick of the paradoxon.

Still, when towards the end - just for s split second - that onlooker takes a breath and stops looking, that's the moment when you reach your granny and overturn her, and he kind of joins the real time again. And that's what mathematical analysis does. Taking a breath at some point, where this breath pretty much equates to what is commonly called "the infinitesimal". And if math wouldn't take it, it'd never find time to write a single meaningful thing down. Just as that onlooker would never do anything else again except keeping on looking.

You and your granny do that footrace and it's already clear that you're going to overturn her in 10 seconds. And at the sideline is that guy looking where you currently are.

As the paradox now devises it, he's going to look faster and faster where you currently are, while you're in the process of catching up. In fact, the speed at which he's looking faster makes it impossible for him to ever finish looking until you have reached your granny. At that point, he's kind of trapped in his own timeline and will never experience the moment when you and your granny meet. Which of course is impossible, so that's basically the mind trick of the paradoxon.

Still, when towards the end - just for s split second - that onlooker takes a breath and stops looking, that's the moment when you reach your granny and overturn her, and he kind of joins the real time again. And that's what mathematical analysis does. Taking a breath at some point, where this breath pretty much equates to what is commonly called "the infinitesimal". And if math wouldn't take it, it'd never find time to write a single meaningful thing down. Just as that onlooker would never do anything else again except keeping on looking.

By weltschmerz - Reply to #371

I'd rather recommend what Pat Corvini observed, as mentioned e.g. here http://en.wikipedia.org/wiki/Zeno%27s_paradox...dern_times

In the real world, only making the realization that Achilles was here or there needs a minimum amount of time that can't become arbitrarily small, and the sum of those times would diverge towards infinity if you don't stop. Put differently, whatever you do, as soon as you don't stop doing it you'll continue endlessly. Whereas the paradox suggests that you could infinitely often do something in finite time, which of course is a misconception.

In the real world, only making the realization that Achilles was here or there needs a minimum amount of time that can't become arbitrarily small, and the sum of those times would diverge towards infinity if you don't stop. Put differently, whatever you do, as soon as you don't stop doing it you'll continue endlessly. Whereas the paradox suggests that you could infinitely often do something in finite time, which of course is a misconception.

So her basic complaint is that mathematics do not directly translate to the laws of physics? Pity that one apparently has to pay to listen to her lecture online :/

Edited by asyyy at 12:25 CST, 1 December 2014

By weltschmerz - Reply to #375

No. Her observation, not complaint, is that Zeno himself makes the switch to physical reality and tries to apply mathematical abstractions where they don't apply.

Example: think of the smallest (edit: positive non-zero obviously) number you can imagine and then divide that by a gazillion taken to the power of itself. And then, with two points - and what is a "point" really in reality - apart that distance, try to distinguish when Achilles crossed the one and not the other.

In this sense the paradoxon is really a good example, of where the mathematical model of time and space having infinite resolution breaks.

Example: think of the smallest (edit: positive non-zero obviously) number you can imagine and then divide that by a gazillion taken to the power of itself. And then, with two points - and what is a "point" really in reality - apart that distance, try to distinguish when Achilles crossed the one and not the other.

In this sense the paradoxon is really a good example, of where the mathematical model of time and space having infinite resolution breaks.

Edited by weltschmerz at 13:00 CST, 1 December 2014

In this sense the paradoxon is really a good example, of where the mathematical model of time and space having infinite resolution breaks.

Ok, I think I get that. She states that while the mathematical model of time and space, being totally abstract, allows infinite resolution breaks, this does not apply to the physical reality, right?

However, I don't get how not being able to distinguish whether or not a distance has been passed says anything about whether or not that distance exists. That does not really sound waterproof to me.

By weltschmerz - Reply to #387

Who talked about the existence of anything? It's about infinitesimal measurements taken in infinitesimal time the paradoxon talks about, and while mathematics might suggest those were theoretically possible the paradoxon shows us how they contradict all our experience.

Of course, some day Achilles and the tortoise might try again and then, maybe, somebody would really be able to tell for an infinite number of points in that finite interval when Achilles crossed which (albeit it might take him some time communicating the info). And then, we actually would have the empirical knowledge that math works on that level too, and the paradoxon wouldn't be any longer a paradoxon.

Of course, some day Achilles and the tortoise might try again and then, maybe, somebody would really be able to tell for an infinite number of points in that finite interval when Achilles crossed which (albeit it might take him some time communicating the info). And then, we actually would have the empirical knowledge that math works on that level too, and the paradoxon wouldn't be any longer a paradoxon.

Edited by weltschmerz at 13:41 CST, 1 December 2014

It's about the existence of an infinite amount of steps inside of a finite interval. One could endlessly break a stick into smaller and smaller pieces. We both agree that this is possible in the physical world, right? So why wouldn't it work the same with time? In an earlier post you stated:

I don't really see how you solve the paradox with that argumentation.

In the real world, only making the realization that Achilles was here or there needsBased on what? Why can't I endlessly break the finite amount of time that it would take Achilles to reach the tortoise into smaller pieces? Like saying, the first action takes 1/2s, the second 1/4s, the third 1/8s, the fourth 1/16s and so on?a minimum amount of time that can't become arbitrarily small, and the sum of those times would diverge towards infinity if you don't stop.

I don't really see how you solve the paradox with that argumentation.

Hi asyyy.

Now first of all let me say that the idea is full of holes from any mathematical conceptual understanding.

Both weltschmerz and (from what I read in this thread Pat Corvini) have very limited understanding of these concepts.

But what they are using in their semi crappy proof is Planck time.

This is famed for being "the smallest measurement of time". Where 1 Planck time = Planck Length / c.

Where Planck Length is then the smallest possible length.

In short (and not 100% correct linguistical use) Planck devised a physical model using infinitesimals.

So what weltschmerz is doing is switching from a system of Reals to a system of Hyperreals, using the infinitesimal nature of the Planck constants and then claiming that the fault of the paradox is that it doesn't make this mistake aswell.

Now first of all let me say that the idea is full of holes from any mathematical conceptual understanding.

Both weltschmerz and (from what I read in this thread Pat Corvini) have very limited understanding of these concepts.

But what they are using in their semi crappy proof is Planck time.

This is famed for being "the smallest measurement of time". Where 1 Planck time = Planck Length / c.

Where Planck Length is then the smallest possible length.

In short (and not 100% correct linguistical use) Planck devised a physical model using infinitesimals.

So what weltschmerz is doing is switching from a system of Reals to a system of Hyperreals, using the infinitesimal nature of the Planck constants and then claiming that the fault of the paradox is that it doesn't make this mistake aswell.

Tbh I'm somewhat in the dark on the exact views of Corvini as well.

But there is 1 simple valid way in which you can say that the physical time cannot be infinitely small.

Which you can simply do by taking the Planck time. As this is regarded (within the field of physics) to be the minimal time possible.

(reason for that is the relation between time, space and properties of light/energy. Which are extremely hard to explain heheh... Also because they are not entirely 'intuitive' but theres a layer of relativity on there which seperates perception from reality (or perhaps better put explains that reality is affected by relativistic effects).)

But there is 1 simple valid way in which you can say that the physical time cannot be infinitely small.

Which you can simply do by taking the Planck time. As this is regarded (within the field of physics) to be the minimal time possible.

(reason for that is the relation between time, space and properties of light/energy. Which are extremely hard to explain heheh... Also because they are not entirely 'intuitive' but theres a layer of relativity on there which seperates perception from reality (or perhaps better put explains that reality is affected by relativistic effects).)

By weltschmerz - Reply to #412

You're almost on track there. Reality isn't necessarily what's happening in our minds or we might be able to think up you know. And math is only as good as it adequately reflects what it's meant to reflect. Achilles represents reality. While the rest of the paradox is math.

Achilles represents reality?

Dude how clueless can you possibly be?

Achilles is a hero of greek myth who was famed for his physical ability.

That's why he was chosen in the paradox to race against a tortoise.

If you were to actually attain the thinking level to come up with such a paradox yourself in the current day you would likely put Usain Bolt against a tortoise.

Dude how clueless can you possibly be?

Achilles is a hero of greek myth who was famed for his physical ability.

That's why he was chosen in the paradox to race against a tortoise.

If you were to actually attain the thinking level to come up with such a paradox yourself in the current day you would likely put Usain Bolt against a tortoise.

By weltschmerz - Reply to #415

In the experiment he represents reality of course. Could have been Cheech and Chong, too. You're determined to turn completely ludicrous now?

By weltschmerz - Reply to #427

The blunt they dropped and that's rolling downhill.

By weltschmerz - Reply to #431

A hill and a seaside, and a party going on in the distance. Doesn't change anything about the main features of the experiment. Abstraction dear fellow. Do occasionally try some, it might benefit you down there in the lab.

Very often the most crucial element of performing a proof is devising the right experiment. And it's not unheard of that specifically during this step some intuition or even a spark of genius can be tremendously helpful.

Very often the most crucial element of performing a proof is devising the right experiment. And it's not unheard of that specifically during this step some intuition or even a spark of genius can be tremendously helpful.

By weltschmerz - Reply to #437

Sorry to disappoint. I'm confident you'll find somebody more fitting to respond to your specific needs before long.

By weltschmerz - Reply to #445

I wouldn't have gone as far as I did if I hadn't been confident that I could rely on your innate benevolence. In particular, I'm fully aware that you're just trying to help me where I'm just helplessly groping about.

By weltschmerz - Reply to #448

Can't blame you, legions have given up on me in the past already. Still, thanks so much for trying. I think I feel a little better already!

Edited by Weird at 19:07 CST, 1 December 2014

By weltschmerz - Reply to #450

Certainly, I totally see your point. Just do me a favor maybe: don't embark on an infinite summation, because I'm quite sure there's people who would like to see you coming back again.

By weltschmerz - Reply to #400

No, you can't endlessly break a stick apart. After so many steps you would reach atomic level. And do you know how many steps were still left at that point to keep breaking it apart endlessly? Infinitely many.

And it's not about breaking time apart. Where you already fall into the trap Zeno presented us with, thinking a mental exercise would adequately reflect reality as we empirically know it.

Also, the paradox isn't "solved". The observation was about where the fallacy may be hidden. Just think about this way for example: the moment Achilles is really close to reaching the tortoise, during the time it takes the light to travel to your eyes to realize how close he is he might already have overtaken it.

And it's not about breaking time apart. Where you already fall into the trap Zeno presented us with, thinking a mental exercise would adequately reflect reality as we empirically know it.

Also, the paradox isn't "solved". The observation was about where the fallacy may be hidden. Just think about this way for example: the moment Achilles is really close to reaching the tortoise, during the time it takes the light to travel to your eyes to realize how close he is he might already have overtaken it.

thinking a mental exercise would adequately reflect reality as we empirically know it

Zeno was a philosopher and as such concerned with thinking outside of "reality as we empirically know it". Beside of that, that same reality has changed quite a lot since then, and will change in the future too.

By weltschmerz - Reply to #410

Sure. But when devising that paradox he let reality slip into his mental exercise when observing that, for all we know from experience, Achilles will overturn the tortoise. He lets a mental exercise "never" clash with an empirical "then". And that then seems to look like a paradox.

to make the direct link to the 0.99999

If Achilles runs at 9km / h (pretty slow for a man but hey)

The tortoise at 0.9km / h (pretty damn fast for a tortoise)

And let's assume that the tortoise has 9 km head start.

After 1 epoch (where 1 epoch = Achilles catching up to where the tortoise was at the start of the epoch)

Achilles would be at 9km and the tortoise at 9.9km from the origional starting point of Achilles.

The next epoch would end when Achilles had ran 9.9km (1h, 6 min) and the tortoise would be at 9.99.

The next when Achilles had ran 9.99km (after 1h, 6m 6s).

And so on untill infinity.

The argument that is made is: because each step take time (as they have to travel) and there are infinitely many steps. You cannot ever reach the tortoise.

The thing that goes wrong is that obviously the time each epoch takes also "limits" towards 0. (I put a limit there to not freak out weltschmerz too much)

While in the paradox this is "hidden away" because it is explained using an epoch rathr than time. And thus this "seems to not be a problem" which causes the confusion.

If Achilles runs at 9km / h (pretty slow for a man but hey)

The tortoise at 0.9km / h (pretty damn fast for a tortoise)

And let's assume that the tortoise has 9 km head start.

After 1 epoch (where 1 epoch = Achilles catching up to where the tortoise was at the start of the epoch)

Achilles would be at 9km and the tortoise at 9.9km from the origional starting point of Achilles.

The next epoch would end when Achilles had ran 9.9km (1h, 6 min) and the tortoise would be at 9.99.

The next when Achilles had ran 9.99km (after 1h, 6m 6s).

And so on untill infinity.

The argument that is made is: because each step take time (as they have to travel) and there are infinitely many steps. You cannot ever reach the tortoise.

The thing that goes wrong is that obviously the time each epoch takes also "limits" towards 0. (I put a limit there to not freak out weltschmerz too much)

While in the paradox this is "hidden away" because it is explained using an epoch rathr than time. And thus this "seems to not be a problem" which causes the confusion.

Edited by Weird at 13:53 CST, 1 December 2014

By weltschmerz - Reply to #396

The one point you might want to take away from all this is that there is no such thing as "infinite sums". Because addition is an operation which takes time to perform. By the same reasoning, and in contrast to what your Wikipedia article says while adding precisely to the confusion that's so widespread already, there's also no decimal with "infinitely many 9s" behind the decimal point.

And mathematical analysis never pretends there was. The approach is exactly to "stop right here because we can't continue to infinity anyway and let that arbitrarily small infinitesimal take care of the rest". That's the ploy, and a nifty one too.

Yet another point you might want to take note of is that the 0.999.. thing isn't in any way special when thinking of it as what it is, namely the series

0.9

0.99

and so on. You can add arbitrary numbers at the end and the series would still converge to 1, like

0.9123

0.995723894759324579357

and so forth.

In fact, for any given number you can easily devise an arbitrary number of series all converging to this given number. In particular, anybody only remotely suggesting that the 0.9 series was in any way a distinguished way of representing 1 in a different manner needs to see a competent math teacher asap.

And mathematical analysis never pretends there was. The approach is exactly to "stop right here because we can't continue to infinity anyway and let that arbitrarily small infinitesimal take care of the rest". That's the ploy, and a nifty one too.

Yet another point you might want to take note of is that the 0.999.. thing isn't in any way special when thinking of it as what it is, namely the series

0.9

0.99

and so on. You can add arbitrary numbers at the end and the series would still converge to 1, like

0.9123

0.995723894759324579357

and so forth.

In fact, for any given number you can easily devise an arbitrary number of series all converging to this given number. In particular, anybody only remotely suggesting that the 0.9 series was in any way a distinguished way of representing 1 in a different manner needs to see a competent math teacher asap.

Edited by weltschmerz at 15:01 CST, 1 December 2014

ok so the point I will take away from this is that you have absolutely no clue what the difference between a number and a numeral is.

Also "addition takes time" is false.

There is a relation of equality between 2 + 2 and 4. Relations do not take any time, they are constructed beforehand.

To compute the sum (through any means) takes times but the operator itself expresses a relation between numbers.

Also "addition takes time" is false.

There is a relation of equality between 2 + 2 and 4. Relations do not take any time, they are constructed beforehand.

To compute the sum (through any means) takes times but the operator itself expresses a relation between numbers.

Edited by Weird at 15:21 CST, 1 December 2014

By weltschmerz - Reply to #402

No, equality is the (equivalence) relation. Addition is the operation. And a sum is what you end up with after performing the operation on its summands.

No need to agree right now. You can thank me later when you feel that the time is right.

No need to agree right now. You can thank me later when you feel that the time is right.

There is a relation of equality between 2 + 2 and 4. Relations do not take any time

Edited by Weird at 15:42 CST, 1 December 2014

By weltschmerz - Reply to #406

You're sounding increasingly weird I"m afraid. I said addition, the operation, took time. Not equality, the relation.

Apart from that, establishing a relation takes time too. Doesn't fall from the sky, you know.

Apart from that, establishing a relation takes time too. Doesn't fall from the sky, you know.

Edited by weltschmerz at 16:05 CST, 1 December 2014

By weltschmerz - Reply to #420

What do you mean with "exists"? As a physical entity?

By weltschmerz - Reply to #426

Well, that ratio doesn't exist within the set of natural numbers for example. It does exist within the set of real numbers thanks to the axiomatic it is based on, a crucial part of which is so called "completeness". And thanks to that "completeness" the set of reals doesn't necessarily exclude numbers only because some of them can't be represented as decimals but only approximated by such.

In the case of pi, that's by the way what people have been doing for many years now. But the common understanding is that the process will never finish. Unless you're willing to accept a certain amount of error of course, a topic I believe I already alluded to briefly.

In the case of pi, that's by the way what people have been doing for many years now. But the common understanding is that the process will never finish. Unless you're willing to accept a certain amount of error of course, a topic I believe I already alluded to briefly.

By weltschmerz - Reply to #438

Gee, you're quite a magician. I don't quite see though why the absence of infinite summation would preclude the existence of pi, which can formally be defined for example as the limit of a series. Care to elaborate?

By weltschmerz - Reply to #443

By weltschmerz - Reply to #451

Why, I thought the point has been covered? You may define 0.99.. to designate a donut. People might still be asking themselves why you'd define it that way and, by the way you chose your notation which is open to other interpretations, arrive at the wrong conclusions.

Seriously, you can define anything any way you want. The question only is how well your definition helps you communicating to others what you want to say.

Seriously, you can define anything any way you want. The question only is how well your definition helps you communicating to others what you want to say.

By weltschmerz - Reply to #454

Did you ask your "bunch of mathematicians" how exactly that 0.99.. would be defined, too? And if, with respect to that definition, somebody suggesting that it was a number with infinitely many digits would have arrived at the right conclusion? If the answer to both questions is yes you may safely send the whole "bunch" back to school. In fact, you really should, in the interest of public safety.

By weltschmerz - Reply to #456

We've been over that already, my friend. It implies a summation 9/10 + 9/10^2 + 9/10^3 and so on that would be infinite. That summation can't be performed, the reason why mathematical analysis exists as it does.

I mean, could you at least step back for a moment and consider why all the stuff you've apparently read about but didn't really digest, like infinitesimals and such, is there at all? Why would we need those strange artifacts if we had decimal representations of numbers with infinite precision?

Math didn't conquer infinity my friend. It just managed to contain it, up to a small detail of varying size that won't entirely vanish. And that precisely to not keep on counting or adding up stuff "til infinity".

I mean, could you at least step back for a moment and consider why all the stuff you've apparently read about but didn't really digest, like infinitesimals and such, is there at all? Why would we need those strange artifacts if we had decimal representations of numbers with infinite precision?

Math didn't conquer infinity my friend. It just managed to contain it, up to a small detail of varying size that won't entirely vanish. And that precisely to not keep on counting or adding up stuff "til infinity".

By weltschmerz - Reply to #460

Within the formalism of mathematical analysis, no. In your inventive mind dreaming about the universe and the role you're meant to occupy in it, maybe yes. But you'd have to tell people what you mean with those numbers.

By weltschmerz - Reply to #463

No, all those numbers can be shown to exist as limits of specific series. Doesn't mean you'd arrive at them by summing up stuff "til infinity", specifically because you'll never arrive at infinity.

Anything else, retard?

Anything else, retard?

nobody other than you ever mentioned "summing up stuff till infinity".

I said that the digits will continue infinitely. Not that you had to sum anything :s

Although tbh it doesn't matter as the sum of 2 numbers equals another number through the relation of equality. Thus you don't have to "perform addition" in math. You only need to perform it if you want to calcualte the other number.

The numeral decimal representation of the number 1/3 = 0.3333...

You are the only person uneducated enough to question this.

You can find this in ANY introduction to mathematics book.

I said that the digits will continue infinitely. Not that you had to sum anything :s

Although tbh it doesn't matter as the sum of 2 numbers equals another number through the relation of equality. Thus you don't have to "perform addition" in math. You only need to perform it if you want to calcualte the other number.

The numeral decimal representation of the number 1/3 = 0.3333...

You are the only person uneducated enough to question this.

You can find this in ANY introduction to mathematics book.

Edited by Weird at 21:20 CST, 1 December 2014

By weltschmerz - Reply to #467

Sorry, that's how decimal numbers are defined. As sums of integers multiplied by powers of ten.

And the 0.333 ... notation isn't a decimal, it's meant to designate the limit of a series of numbers and, in this notation, is a misleading representation of that limit. You can tell it's misleading because there's clowns like you thinking it was a sum of infinitely many summands.

Did your mom also have to repeat everything 20 times to you?

And the 0.333 ... notation isn't a decimal, it's meant to designate the limit of a series of numbers and, in this notation, is a misleading representation of that limit. You can tell it's misleading because there's clowns like you thinking it was a sum of infinitely many summands.

Did your mom also have to repeat everything 20 times to you?

My mom didn't teach me math.

I can see where this is going... Your mom is janitor at that university you linked me to, and she taught you math by repeating digits to you.

I'm sorry man but I'm not wrong about this, you are.

If you want you can buy any book on maths and iyou can read for yourself that I'm right.

I can see where this is going... Your mom is janitor at that university you linked me to, and she taught you math by repeating digits to you.

I'm sorry man but I'm not wrong about this, you are.

If you want you can buy any book on maths and iyou can read for yourself that I'm right.

Edited by Weird at 21:29 CST, 1 December 2014

By weltschmerz - Reply to #470

You mean I should consider your "introductory calculus for the regular clown" series for a round of corrections?

By weltschmerz - Reply to #474

Run out of own words?

By weltschmerz - Reply to #469

The "by definition" part is precisely the point. And the other part worth observing might be that in some cases, like pi, the number can merely be shown to exist, because there's series converging to it in the sense of becoming arbitrarily close, while a converging series can be proven to have a limit and a unique one.

Nobody will ever see how such a number exactly looks like though, and never arrive at it by doing something by "continuing til infinity", the main occupation of our genius here (as I just could personally verify beyond any margin of error).

Nobody will ever see how such a number exactly looks like though, and never arrive at it by doing something by "continuing til infinity", the main occupation of our genius here (as I just could personally verify beyond any margin of error).

Edited by weltschmerz at 21:36 CST, 1 December 2014

By weltschmerz - Reply to #473

Interesting. Then pray share, what would be your idea of a number? Feel free to define. And, while at it, what's your idea of a decimal?

Well let's just say what a number is not:

A number is NOT the numeral representation of the number.

We identify a numer by a numeral but it is just an entity representing an abstract value.

Nor is it the numeral value of a limit of some series.

It is more abstract than that.

A decimal can be multiple things depending on the way you phrase words.

For a fun read: http://en.wikipedia.org/wiki/Decimal

I would suggest that you also read the Non-uniqueness of decimal representation.

A number is NOT the numeral representation of the number.

We identify a numer by a numeral but it is just an entity representing an abstract value.

Nor is it the numeral value of a limit of some series.

It is more abstract than that.

A decimal can be multiple things depending on the way you phrase words.

For a fun read: http://en.wikipedia.org/wiki/Decimal

I would suggest that you also read the Non-uniqueness of decimal representation.

By weltschmerz - Reply to #477

Well, for starters, let's say a number would be an element from one of the main sets of numbers known to man, like the natural numbers, the integrals, the rationals, real and complex numbers. Would that be a reasonable start and maybe make it a little less abstract for you? Feel free to continue from there and share some insights.

The other part is exactly what I'm talking about. And since it says "this section needs additional citations for verification" maybe you're expecting me now to spend some time correcting?

The other part is exactly what I'm talking about. And since it says "this section needs additional citations for verification" maybe you're expecting me now to spend some time correcting?

Edited by weltschmerz at 22:11 CST, 1 December 2014

Ofcourse that's a reasonably start. Each of those sets has certain rules as to how you can write down a number.

The set of reals for instance allows for 0.999... to write down 1, which is defined as a unit. (often a unit vector but I don't wanna bother you with vectors)

The set of reals for instance allows for 0.999... to write down 1, which is defined as a unit. (often a unit vector but I don't wanna bother you with vectors)

Edited by Weird at 22:15 CST, 1 December 2014

By weltschmerz - Reply to #481

Dear me. It's kind of embarrassing for me to remind you, but anybody not clown would hardly talk of a unit vector in the context of real numbers. As a vector space, in general, is an abelian group with a field operating on it. And since the "unit" 1 is generally understood to be the neutral element of multiplication and zero that of addition, and since an abelian group merely defines addition, the group in general doesn't have a "1".

One may talk of a unit vector in case of additional structure, when the vector space for example is supplied with a metrics e.g. in form of a scalar product. But then this "unit" would designate the length of the vector according to the metrics, namely the length having the real number value 1. Is that what you're trying to communicate, that the real number 1 has the length 1? Amazing insights you keep sharing.

And the set of reals for example also allows for askjfowetr to denote 1. I can just define it that way, as little sense as it might make to you. Just like other notations make pretty little sense.

One may talk of a unit vector in case of additional structure, when the vector space for example is supplied with a metrics e.g. in form of a scalar product. But then this "unit" would designate the length of the vector according to the metrics, namely the length having the real number value 1. Is that what you're trying to communicate, that the real number 1 has the length 1? Amazing insights you keep sharing.

And the set of reals for example also allows for askjfowetr to denote 1. I can just define it that way, as little sense as it might make to you. Just like other notations make pretty little sense.

By weltschmerz - Reply to #487

Did they teach you the complex numbers as vector space? Didn't know they still did that in the "introductory calculus for clowns" series, mixing up R2 and C. No wonder you're appearing to be confused in every which way.

By weltschmerz - Reply to #493

2-tuples of real numbers with an extra element i and some multiplication rules besides the obvious element wise operations. And where's the vector space now you believe would play any role in the theory of complex numbers?

By weltschmerz - Reply to #506

Let's first settle the vector space nonsense you're spreading around before educating you on other things.

So 1 is "the unit vector" of C, the set of complex numbers. Which should make you wonder what a "unit vector" is supposed to be at all, and I trust you're having something wacky coughed up in your mind for that. And then, seeing how it is "the" unit vector in your terminology, how by all means it is supposed to be unique or distinguished?

I for example know the unit "spheres" of R, R2, R3 and so on, spaces equipped with a metrics, to be defined as the sets of all elements with length 1. Which results in the circle S1 as the sphere in R2. The sphere S2 in R3, which we commonly understand as sphere. And for example the sphere S0 in R. And can you guess how many elements S0 contains?

So then, what's a unit vector at all supposed to mean in C. And why do you think there would be a distinguished "the unit vector"? Pray share those insights you may trust the whole math community would be curious to hear in case there was only the slightest hint of meaning attached to them.

So 1 is "the unit vector" of C, the set of complex numbers. Which should make you wonder what a "unit vector" is supposed to be at all, and I trust you're having something wacky coughed up in your mind for that. And then, seeing how it is "the" unit vector in your terminology, how by all means it is supposed to be unique or distinguished?

I for example know the unit "spheres" of R, R2, R3 and so on, spaces equipped with a metrics, to be defined as the sets of all elements with length 1. Which results in the circle S1 as the sphere in R2. The sphere S2 in R3, which we commonly understand as sphere. And for example the sphere S0 in R. And can you guess how many elements S0 contains?

So then, what's a unit vector at all supposed to mean in C. And why do you think there would be a distinguished "the unit vector"? Pray share those insights you may trust the whole math community would be curious to hear in case there was only the slightest hint of meaning attached to them.

well that's a somewhat philosophical question.

And a lot of people have a similar description for it as they all mean to describe the same concept, but it is a very abstract concept.

Because a "unit" of length would be a meter. A unit vector (of length) would be a meter into a direction.

So the unit is a reference to a single entity that you use in order to describe other entities with.

The unit vector of numbers is called 1. In a "mathematical plane" (which is a choice of words that I use to try and describe an abstract concept to you) this would be related in the same way to the mathematical plane as a meter is related to distance.

Now I'm not saying that somehow 1 represents a distance. It represents a unit. Seeing how people are familliar with distances the relation of a unit vector in math is the same relation as the one between distance and meter into a direction.

And a lot of people have a similar description for it as they all mean to describe the same concept, but it is a very abstract concept.

Because a "unit" of length would be a meter. A unit vector (of length) would be a meter into a direction.

So the unit is a reference to a single entity that you use in order to describe other entities with.

The unit vector of numbers is called 1. In a "mathematical plane" (which is a choice of words that I use to try and describe an abstract concept to you) this would be related in the same way to the mathematical plane as a meter is related to distance.

Now I'm not saying that somehow 1 represents a distance. It represents a unit. Seeing how people are familliar with distances the relation of a unit vector in math is the same relation as the one between distance and meter into a direction.

Edited by Weird at 12:03 CST, 2 December 2014

By weltschmerz - Reply to #517

Do you realize that you just offered your head on a silver platter?

Edited by weltschmerz at 12:10 CST, 2 December 2014

By weltschmerz - Reply to #525

Well, then how, for starters, would you explain that a unit vector, defined to have length 1 by you, is supposed to define 1 itself? Kind of a circular definition, isn't it.

Maybe one of the extremely tough philosophical problems you've got to tackle in your everyday life?

Maybe one of the extremely tough philosophical problems you've got to tackle in your everyday life?

If I define you to be a braindead idiot. Then the definition of a braindead idiot isn't automatically weltschmerz is it?

But if I want to explain to someone what a braindead idiot is... I can point to you and say "here is someone who represents the whole group of braindead idiots".

So if I define 1 to represent a number which represents the unit of all numbers.

That doesn't mean that I have to define any length.

Just like the "length" of 1 meter could've just as well been equal to what we now call a centimeter, or equal to an inch or a foot or any other length you wish it to have. The only issue is that when you measure something after having redefined the unit.... you end up with a different measurement in units.

To even say this more simplistic: if your dick is 5cm in length, and we then measure it in inches it's suddenly 2inch. Meanwhile you can pray for it to get longer.... but the actual size won't change, the measurement is dependant on the scale though.

We can further show this same concept by saying that on my scale where you might be a braindead idiot, obi is actually pretty smart. But on your scale where I am a braindead idiot you yourself might be an atom and obi a molecule. (I'm somewhat exaggerating here)

But if I want to explain to someone what a braindead idiot is... I can point to you and say "here is someone who represents the whole group of braindead idiots".

So if I define 1 to represent a number which represents the unit of all numbers.

That doesn't mean that I have to define any length.

Just like the "length" of 1 meter could've just as well been equal to what we now call a centimeter, or equal to an inch or a foot or any other length you wish it to have. The only issue is that when you measure something after having redefined the unit.... you end up with a different measurement in units.

To even say this more simplistic: if your dick is 5cm in length, and we then measure it in inches it's suddenly 2inch. Meanwhile you can pray for it to get longer.... but the actual size won't change, the measurement is dependant on the scale though.

We can further show this same concept by saying that on my scale where you might be a braindead idiot, obi is actually pretty smart. But on your scale where I am a braindead idiot you yourself might be an atom and obi a molecule. (I'm somewhat exaggerating here)

Edited by Weird at 12:54 CST, 2 December 2014

By weltschmerz - Reply to #527

Well, sweetie, you said "trust me 1 is the unit vector." And you said "because a unit of length would be a meter" where - in your case we really have to make sure - "a meter" is supposed to mean one meter, no? Which reminds me of that guy who tried sticking his head up his ass so that it might come back out of his mouth.

No clue what any measure, like meters, has to do with this anyhow, seeing that those are part of physics and not of math, but I guess that's presumably yet another one of those extremely tough to explain philosophical problems.

So, clown, be informed that in any multiplicative group 1 is defined to be the neutral element of multiplication. Any philosophical idea what that might mean?

No clue what any measure, like meters, has to do with this anyhow, seeing that those are part of physics and not of math, but I guess that's presumably yet another one of those extremely tough to explain philosophical problems.

So, clown, be informed that in any multiplicative group 1 is defined to be the neutral element of multiplication. Any philosophical idea what that might mean?

By weltschmerz - Reply to #531

You know what the real problem is? The real problem is that you're the type of guy having a vague clue about math at best but who likes to pretend it was different and, when called out, starts becoming more and more fuzzy, hiding behind pseudo philosophical crap and excuses while making a tough subject still more confusing for those who really try to understand something. Just to somehow save your dumb, pretentious face.

At the core of this behavior of course is a character flaw, which might be forgivable to some extent. What I personally don't forgive though is this blatant and fundamentally counterproductive abuse of mathematics you're exacting for your personal, shitty purposes.

So, besides about the definition of 1, be informed about something else, namely that I'm having you noted down in my book permanently as an ahole as complete as one could ever ask for.

At the core of this behavior of course is a character flaw, which might be forgivable to some extent. What I personally don't forgive though is this blatant and fundamentally counterproductive abuse of mathematics you're exacting for your personal, shitty purposes.

So, besides about the definition of 1, be informed about something else, namely that I'm having you noted down in my book permanently as an ahole as complete as one could ever ask for.

I see. And what is the standard mathematical definition of a "unit vector"?

Edited by obi at 13:17 CST, 2 December 2014

By weltschmerz - Reply to #480

It's a sum. And the operation of summation can performed in a limited amount of time only when the set of summands is finite.

Didn't we discuss that already? You might claim that something was an "infinite sum", but by definition it's something else, namely the limit of a series. And as such, a decimal with an infinite number of digits is misleading notation. You already observed yourself that a so called "infinite sum" isn't really an infinite sum by definition.

Didn't we discuss that already? You might claim that something was an "infinite sum", but by definition it's something else, namely the limit of a series. And as such, a decimal with an infinite number of digits is misleading notation. You already observed yourself that a so called "infinite sum" isn't really an infinite sum by definition.

I guess I just don't understand why you would make some kind of qualitative judgement about what it "really is". When faced with the concept of infinite summation, we can either say it's undefined or extend the definition and both choices are ultimately arbitrary. Once we have it defined, a decimal with infinite digits has a clear meaning.

By weltschmerz - Reply to #488

It wasn't about the meaning. It was about what the notation suggests how we arrive at that meaning. I know what it means. You presumably too. But our friend here, there I'm already having serious doubts.

Again, the notation suggests it was a sum. Which induces the wrong idea, it's the limit of a series. Where the precise process of "taking a limit", and how this process would behave under operations like taking functions, has to be precisely understood to properly use analytical math. And that notation doesn't contribute anything to that, on the contrary. It gives the wrong idea.

Ok, I'm not going to repeat again what I've already said that many times.

Again, the notation suggests it was a sum. Which induces the wrong idea, it's the limit of a series. Where the precise process of "taking a limit", and how this process would behave under operations like taking functions, has to be precisely understood to properly use analytical math. And that notation doesn't contribute anything to that, on the contrary. It gives the wrong idea.

Ok, I'm not going to repeat again what I've already said that many times.

By weltschmerz - Reply to #492

You know, the key point when "taking limits" is that you never "continue til infinity". You know the limit is there. You know you can get arbitrarily close. And if you need to compute something you get yourself a decimal that's as close as you need for the precision you desire.

Now let's take pi. You know the series, lets say a(1) a(2) a(3) ..., with which you can get close. But what if you want to compute the square of pi? At this point you have to remember precisely how you defined it, namely as limit of that series. Then you have to ask yourself: well, if a(n) approaches pi, would the squares of a(n) approach the square of pi too? Because if they did you have decimals you can work with again to the precision you desire.

Turns out, for the square function it works, because it's "continuous". But it doesn't work in general at all, and you can experience the most nasty surprises in that area. Which means that, when replacing a series with it's limit, you have to be very, very careful when applying any operations in the process.

And that's why I said the 0.99 notation induces the wrong idea, as our friend here said it was a number with infinitely many digits. Because it entirely obscures the actual process that makes mathematical analysis tick. And it's less than helpful in giving you a hint about what methods you'd have to apply when trying to perform calculations on your own.

Now let's take pi. You know the series, lets say a(1) a(2) a(3) ..., with which you can get close. But what if you want to compute the square of pi? At this point you have to remember precisely how you defined it, namely as limit of that series. Then you have to ask yourself: well, if a(n) approaches pi, would the squares of a(n) approach the square of pi too? Because if they did you have decimals you can work with again to the precision you desire.

Turns out, for the square function it works, because it's "continuous". But it doesn't work in general at all, and you can experience the most nasty surprises in that area. Which means that, when replacing a series with it's limit, you have to be very, very careful when applying any operations in the process.

And that's why I said the 0.99 notation induces the wrong idea, as our friend here said it was a number with infinitely many digits. Because it entirely obscures the actual process that makes mathematical analysis tick. And it's less than helpful in giving you a hint about what methods you'd have to apply when trying to perform calculations on your own.

By weltschmerz - Reply to #498

It suggests you could do something indefinitely, like constructing a decimal with infinitely many digits. That's how the whole thing started out, the clown saying exactly that. Which is wrong.

If it was possible, I could by the same reasoning take the series, which is infinite, and then take out any number that is not equal 1 "continuing til infinity" until nothing is left. Thanks to my ability to continue that long I arrive at the empty set. And is that then supposed to be equal to 1, after I've checked every number and verified that it wasn't? Doesn't make much sense does it.

Mathematical analysis is finite, because all we can do has to be done with finitely many steps in finite time. It still tries to somehow handle infinity though and, in some cases of interest, manages to do so up to an arbitrarily small amount of error that never vanishes, not in reality and also not in the theory.

When talking about pi anywhere for example it's never forgotten that we only can approximate it and never will "see" it. And anybody writing for example "pi = 3.14.." did not only not understand what the whole thing was about but is also spreading his misunderstanding. He may say that 3.14... gets arbitrarily close to pi. But if he wanted an equal sign he had to write lim 3.14.. = pi and then understand what the "lim" part is supposed to say.

If it was possible, I could by the same reasoning take the series, which is infinite, and then take out any number that is not equal 1 "continuing til infinity" until nothing is left. Thanks to my ability to continue that long I arrive at the empty set. And is that then supposed to be equal to 1, after I've checked every number and verified that it wasn't? Doesn't make much sense does it.

Mathematical analysis is finite, because all we can do has to be done with finitely many steps in finite time. It still tries to somehow handle infinity though and, in some cases of interest, manages to do so up to an arbitrarily small amount of error that never vanishes, not in reality and also not in the theory.

When talking about pi anywhere for example it's never forgotten that we only can approximate it and never will "see" it. And anybody writing for example "pi = 3.14.." did not only not understand what the whole thing was about but is also spreading his misunderstanding. He may say that 3.14... gets arbitrarily close to pi. But if he wanted an equal sign he had to write lim 3.14.. = pi and then understand what the "lim" part is supposed to say.

Edited by weltschmerz at 11:07 CST, 2 December 2014

I think in the end it comes down to whether mathematics describe something that exists or whether it is used to create something new, artificial. And if there is a concept of infinity to be found in the nature of the universe, why shouldn't it be possible to represent it in mathematics? In my opinion you are way too much concerned with what one does with their mind (observing, realizing, measuring.. everything takes > 0 timeunits of course) and miss out on the notion of concepts simply existing in an abstract way.

But that's just my opinion and I honestly don't try to convince you of anything.

But that's just my opinion and I honestly don't try to convince you of anything.

By weltschmerz - Reply to #457

As a general rule, mathematics per se doesn't describe anything physically existing at all. It's a pure model, an invention, based on axioms that are postulated and not even really supposed to be "true", but hopefully meaningful in one way or another to make mathematics serve a purpose, like model our world to some useful extent.

And infinity is defined in mathematics, even in countable and uncountable variants. Doesn't mean that anybody assumes he could indefinitely perform an operation on a number, for example.

And infinity is defined in mathematics, even in countable and uncountable variants. Doesn't mean that anybody assumes he could indefinitely perform an operation on a number, for example.

It's a pure model, an invention, based on axioms that are postulated and not even really supposed to be "true", but hopefully meaningful in one way or another to make mathematics serve a purpose, like model our world to some useful extent.

Well, that's your opinion. And btw, I was not talking about anything physical, but abstract concepts.

By weltschmerz - Reply to #462

No, any mathematical theory is based on axioms which are mere postulations. And there's been substantial work done already on the question if we can be sure of those to make sense at all. See Gödel for example, who has shown that no nontrivial theory can even be proven to be contradiction-free.

Oh wait - that's probably Gödel's opinion.

Oh wait - that's probably Gödel's opinion.

which equality exactly?

?

wassup, you don't agree that 2 + 2 = 4?

You can see the = as a relationship of equality.

As in 2 + 2 is equal to 4.

It's not like you have to "have 2, then add 2 and come up with 4".

To perform the operator + is called solving an equation. Where the problem is 2 + 2 = X.

And the question asked is "what is X?"

Where your 'job' is to search through all possible X to come up with 4 as the only fit candidate for X.

Eventually leading to you claiming equality (for this problem) between X and 4.

Do you have any question about that?

wassup, you don't agree that 2 + 2 = 4?

You can see the = as a relationship of equality.

As in 2 + 2 is equal to 4.

It's not like you have to "have 2, then add 2 and come up with 4".

To perform the operator + is called solving an equation. Where the problem is 2 + 2 = X.

And the question asked is "what is X?"

Where your 'job' is to search through all possible X to come up with 4 as the only fit candidate for X.

Eventually leading to you claiming equality (for this problem) between X and 4.

Do you have any question about that?

So it only work with said numbers (0.9 / 0.99) and only if you observe each element at a time, if you imagine them both simultaneously traveling you get a finite point, the one where both

I think you explanation makes the most sense, although I read the links provided.

Honestly for me it's just hard to comprehend because I try to apply real life situations and don't imagine it as a mathematical nonexistent universe.

I think you explanation makes the most sense, although I read the links provided.

Honestly for me it's just hard to comprehend because I try to apply real life situations and don't imagine it as a mathematical nonexistent universe.

By weltschmerz - Reply to #409

The 0.9 thing was a different discussion about whether anybody could do anything "til infinity". And I brought up the paradox originally only to show how this assumption leads to nonsensical conclusions or contradictions.

The point with the paradox really is that it devises a scenario where anybody could know that Achilles was at a certain "point", and this infinitely often in a limited amount of time. Which might be imaginable in our minds - albeit not really because even in our minds we cut infinity short with an "and so on" - while reality has told us so far that it isn't possible. And that's what has been baffling people until now and continues to do so. Kind of an ongoing "reality check".

The point with the paradox really is that it devises a scenario where anybody could know that Achilles was at a certain "point", and this infinitely often in a limited amount of time. Which might be imaginable in our minds - albeit not really because even in our minds we cut infinity short with an "and so on" - while reality has told us so far that it isn't possible. And that's what has been baffling people until now and continues to do so. Kind of an ongoing "reality check".

By asdfasdfasdf - Reply to #300

did you know that 1/3 in ternary is .1?

You are untrained in Mathematics and really ignorant about how things like algebras and number systems are constructed, yet here you are pontificating on the true meaning of Mathematical thought and what Maths is "really about". You are incredibly egotistical, your level of reading comprehension is extremely low and honestly I think you suffer from some form of autism.

Right.....

So because you cannot read and think I am stupid / autistic.

Great world you live in... Perhaps you should buy a mirror?

Dude you should be paying me for trying to make your brain function like a normal brain. Not insult me.

Heck I've spend more than enough time on you. You are a hopeless case.

You're one of those people who gets upset when they discover how stupid they are and then just throw around insults to the people who pointed this out.

It's a good thing that this has never happened to me irl :D

So because you cannot read and think I am stupid / autistic.

Great world you live in... Perhaps you should buy a mirror?

Dude you should be paying me for trying to make your brain function like a normal brain. Not insult me.

Heck I've spend more than enough time on you. You are a hopeless case.

You're one of those people who gets upset when they discover how stupid they are and then just throw around insults to the people who pointed this out.

It's a good thing that this has never happened to me irl :D

I guess physically he could... A somewhat educated guess would be that physically you can beat me up as well.

Seeing how I, like my dad, have spend virtually all my time at increasing my knowledge and skills in sciences and you obviously did not.

So you must've had enough time to work out, learn how to fight.

I found a pretty decent equilibrium lately though where I do end up doing quite a bit of sports each week.

Seeing how I, like my dad, have spend virtually all my time at increasing my knowledge and skills in sciences and you obviously did not.

So you must've had enough time to work out, learn how to fight.

I found a pretty decent equilibrium lately though where I do end up doing quite a bit of sports each week.

Except he's not using the extended number line, he's stated that some of those operation are not valid. He'll never formally define what he's on about because he is not able to. He doesn't even understand what it means to define something.

Edited by obi at 13:39 CST, 29 November 2014

By weltschmerz - Reply to #212

Make love not war.

I find it mindboggling how you always seek fault in other people and aim to consistently insult them. Even though you don't know them nor have the mental capability to understand them.

ah my loyal fan ;)

You don't really have to join in on this and pick a side though...

It'll be better for you if you sit this one out.

You don't really have to join in on this and pick a side though...

It'll be better for you if you sit this one out.

Where? I don't see it. Let me guess, its defined by

0.999...(8) = (1 - 0) - 0

lol

Also how do you reconcile the fact that

1 - 0 = 0.999...

1 - 0 != 1

and

1 = 0.999... (by definition. Or are you going to redefine how limits work?)

0.999...(8) = (1 - 0) - 0

lol

Also how do you reconcile the fact that

1 - 0 = 0.999...

1 - 0 != 1

and

1 = 0.999... (by definition. Or are you going to redefine how limits work?)

Edited by obi at 14:40 CST, 29 November 2014

I said that you can view it as if that the 'infinith digit' of the number is the one between ().

Ofcourse there is no infinith digit, which allows me to add in this notation without seriously breaking anything....

I figured that someone like you could perhaps think about the problem like this rather than in a more abstract way.

But it appears that you don't want to think at all.

And how else would you want me to define mathematics if not through equality?

Ofcourse there is no infinith digit, which allows me to add in this notation without seriously breaking anything....

I figured that someone like you could perhaps think about the problem like this rather than in a more abstract way.

But it appears that you don't want to think at all.

And how else would you want me to define mathematics if not through equality?

complex numbers are in an imaginairy plane.... yet they are useful.

It's not that because something doesn't exist that it can't be used in math.

I never saw anyone count to infinity.... yet it exists in math as a useful concept.

Perhaps I could urge you to attempt counting to infinity.... that way you won't bother me all the time.

It's not that because something doesn't exist that it can't be used in math.

I never saw anyone count to infinity.... yet it exists in math as a useful concept.

Perhaps I could urge you to attempt counting to infinity.... that way you won't bother me all the time.

complex numbers are in an imaginairy plane.... yet they are useful.I never said anything like that. Imaginary numbers are useful because they are consistent and well-defined.

It's not that because something doesn't exist that it can't be used in math.

A number with 8 as the "infinith" digit (which doesn't exist) is

By Nuked User - Reply to #157

* N U K E D *

By asdfasdfasdf - Reply to #138

Edited by brandan at 23:02 CST, 27 November 2014

By asdfasdfasdf - Reply to #146

i hope you'll accept this as sufficient evidence:

https://www.esreality.com/post/2348591#pid2362615

click the dropbox link for a special message.

https://www.esreality.com/post/2348591#pid2362615

click the dropbox link for a special message.

If you're curious about the earth's orbit though I would suggest you to think about the following:

If time flows faster on one side of an object than on the other side of the same object, does it bend in space?

Aka you have "empty space" with 2 objects in it.

These 2 objects do not have any velocity at the start of the 'thought experiment'.

Newton claims that these objects attract eachother and thus start moving.

Einstein claims that "mass bends space-time" making time "near an object" move faster.

And thus the time "in between the objects" runs at a certain delta (gravitational force) faster.

Now repeat the same thought experiment but give both of the objects a non-changing velocity. You'll see that it eventually will find an orbit around the other object. (It may be easiest if you "fix a large object at a certain place in your thought experiment" and let a small object fly past at a constant pace....)

edit: my phrasing using the "gravitational force" can be confusing.... You should look at it similarly as Feynman's explanation as to why light appears to move in a straight line while infact it moves everywhere.... By which I mean that the total amounted difference would be the delta... so it's not 1 straight line between the objects that is affected but it's a gradual 'fade out' of which the sum would be the singular gravitational vector in space.

If time flows faster on one side of an object than on the other side of the same object, does it bend in space?

Aka you have "empty space" with 2 objects in it.

These 2 objects do not have any velocity at the start of the 'thought experiment'.

Newton claims that these objects attract eachother and thus start moving.

Einstein claims that "mass bends space-time" making time "near an object" move faster.

And thus the time "in between the objects" runs at a certain delta (gravitational force) faster.

Now repeat the same thought experiment but give both of the objects a non-changing velocity. You'll see that it eventually will find an orbit around the other object. (It may be easiest if you "fix a large object at a certain place in your thought experiment" and let a small object fly past at a constant pace....)

edit: my phrasing using the "gravitational force" can be confusing.... You should look at it similarly as Feynman's explanation as to why light appears to move in a straight line while infact it moves everywhere.... By which I mean that the total amounted difference would be the delta... so it's not 1 straight line between the objects that is affected but it's a gradual 'fade out' of which the sum would be the singular gravitational vector in space.

Edited by Weird at 23:32 CST, 27 November 2014

By asdfasdfasdf - Reply to #149

the objects will actually orbit a shared barycenter, and i'm not sure what this thought experiment does for me.

btw, the original drawing in that dropbox link was of earth orbiting the sun on a plane, with some dash lines to illustrate a concept of shifting orbital inclination. i didn't have the vocabulary to search well at the time, but i think i remember finding the correct terms within a few hours of the post. there's an interesting link in this comment related to the how the concept impacts life on earth.

btw, the original drawing in that dropbox link was of earth orbiting the sun on a plane, with some dash lines to illustrate a concept of shifting orbital inclination. i didn't have the vocabulary to search well at the time, but i think i remember finding the correct terms within a few hours of the post. there's an interesting link in this comment related to the how the concept impacts life on earth.

Edited by brandan at 23:53 CST, 27 November 2014

In your referenced post you say:

"hi. i actually drew something like this recently when i was thinking about the nature of matter in the universe and how that applies to the earth's orbit:"

This way of thinking links "the nature of matter" to the earth's orbit.

Most people say that "gravity bends space-time" but you could also say the almost exact opposite "gravity is the bend in space time which is caused by mass".

Both are completely interchangable.

However the later way of thinking will give a much more "simple explanation" as to why orbits are the way they are and why planets rotate the same way.*

*not all planets do rotate the same way.... But venus is slowing down it's "opposite rotation". And the planets further on seem to be getting into an equilibrium where they also move similarly to the other planets. (in general they wobble a bit more ;p)

"hi. i actually drew something like this recently when i was thinking about the nature of matter in the universe and how that applies to the earth's orbit:"

This way of thinking links "the nature of matter" to the earth's orbit.

Most people say that "gravity bends space-time" but you could also say the almost exact opposite "gravity is the bend in space time which is caused by mass".

Both are completely interchangable.

However the later way of thinking will give a much more "simple explanation" as to why orbits are the way they are and why planets rotate the same way.*

*not all planets do rotate the same way.... But venus is slowing down it's "opposite rotation". And the planets further on seem to be getting into an equilibrium where they also move similarly to the other planets. (in general they wobble a bit more ;p)

By asdfasdfasdf - Reply to #154

i think my original (referenced) post is unclear (particularly 'the nature of matter and its blah blah' sentence) and confusing my original intent. the original dropbox drawing clarified what i was asking.

Edited by brandan at 23:58 CST, 27 November 2014

By asdfasdfasdf - Reply to #151

here is the post where i ended up finding some cool links.

Damn dude, that stuff looks complicated ;)

I'm not gonna look at it at 7 at night (damn it's morning.......) after having a few drinks.

I like simple concepts and then apply them broadly....

The simple concept is relativity... and it explains all of these things (because otherwise one of these things would be used to disprove relativity*).

* the lack of the disprovence of relativity through any of these aspects doesn't necesarily prove my point, but given how much criticism and scientific testing the theory of relativity has been though it makes a substancial case for my point.

My point being that these things are effects explainable through relativity, rather than effects on their own that need a seperate theory.

I'm not gonna look at it at 7 at night (damn it's morning.......) after having a few drinks.

I like simple concepts and then apply them broadly....

The simple concept is relativity... and it explains all of these things (because otherwise one of these things would be used to disprove relativity*).

* the lack of the disprovence of relativity through any of these aspects doesn't necesarily prove my point, but given how much criticism and scientific testing the theory of relativity has been though it makes a substancial case for my point.

My point being that these things are effects explainable through relativity, rather than effects on their own that need a seperate theory.

By juan_juanson - Reply to #37

I wasn't suggesting you were pissed. I was pointing out that a lot of players were apparently pissed off about the Steam changes -- and understandably so, for the old school guys. My point was that unlike the "steam update", these rumored changes don't mess with the gameplay and could provide a significant benefit.

By juan_juanson - Reply to #47

Naw.... Not familiar with who you are or what you've posted on here, aside from posts in the netcode thread (which included some interesting observations).

Edited by agentsmith_ at 17:18 CST, 25 November 2014

Yeah, but for the "old school" guys this news is meaningless. Unless they revert the previous steam update to what it was before.

Myself, I haven't touched qlive since a day before the steam update. And them going steam exclusive won't change any of the shitfest they created with said update. For me it just means going from 99.9% I won't play qlive in it's current form to 100% not playing it in it's soon to be new form.

Myself, I haven't touched qlive since a day before the steam update. And them going steam exclusive won't change any of the shitfest they created with said update. For me it just means going from 99.9% I won't play qlive in it's current form to 100% not playing it in it's soon to be new form.

By Anonymous (79.168.55.112) - Reply to #43

what rumor changes. nothing in op

By juan_juanson - Reply to #60

If you search for the URL on google you get a small excerpt of what was posted, but there's no full cached version.

Great news.

I don't have anything against Steam.

Sad part is that they will kill qlranks service. Hopefully they will not.

Maybe they will start to use Valve anti cheat.

But I doubt that Valve is capable to catch quakelive smart aimbots.

Radiant its cool stuff. Reflex has it built in )

I don't have anything against Steam.

Sad part is that they will kill qlranks service. Hopefully they will not.

Maybe they will start to use Valve anti cheat.

But I doubt that Valve is capable to catch quakelive smart aimbots.

Radiant its cool stuff. Reflex has it built in )

By MajkiFajki - Reply to #7

Radiant its cool stuff. Reflex has it built in

Comparing Reflex Editor to Radiant is like comparing bicycle to F-16.

And you can clip a baseball card onto the frame so it hits the spokes and makes the click/tick sound. Can't do none of that on an F-16.

By juan_juanson - Reply to #7

Yeah...... It has to be Steam-only if a developer wants to use VAC. They aren't going to be able to develop their own anticheat due the cost and complexity. Not sure if the rumor is true but it makes sense to me.

VAC would actually be quite effective against the 2 or 3 free aimbot programs that have been plaguing the game for quite a while. It's effective at identifying any "known" cheat programs. It won't be as effective against the custom paid hacks a few people use, but 95%+ of cheaters are using free, identifiable hacks.

VAC would actually be quite effective against the 2 or 3 free aimbot programs that have been plaguing the game for quite a while. It's effective at identifying any "known" cheat programs. It won't be as effective against the custom paid hacks a few people use, but 95%+ of cheaters are using free, identifiable hacks.

Edited by agentsmith_ at 15:29 CST, 25 November 2014

Edited by gluttony at 02:10 CST, 25 November 2014

By juan_juanson - Reply to #83

...

Edited by agentsmith_ at 16:28 CST, 26 November 2014

qlranks is the only positive thing made for ql in years, rotfl @ this update

Yeah I don't really understand when all the features the game need are being made by the community if possible and every time it is id's turn to add something, it seems like a big screw up. At least, that's what it is for the changes we have received lately.

Over the years, they could have added a basic league / leaderboard implemention and hone it over the time. Queuing system or a PUG system. Anything at all that would have helped Quake stay true as an eSport and not the kind of changes that are valuable for a casual game.

It seems like this is our current problem, they are not considering Quake as an eSport anymore. They can still monetize the game without sacrificing its most crucial aspect. :(

Over the years, they could have added a basic league / leaderboard implemention and hone it over the time. Queuing system or a PUG system. Anything at all that would have helped Quake stay true as an eSport and not the kind of changes that are valuable for a casual game.

It seems like this is our current problem, they are not considering Quake as an eSport anymore. They can still monetize the game without sacrificing its most crucial aspect. :(

They never considered quake as an esport.

Also esport doesn't exist - there is merely "competetive gaming".

Also esport doesn't exist - there is merely "competetive gaming".

By Anonymous (79.168.55.112) - Reply to #25

syncerror call ql esport. i saw this

By Anonymous (79.168.55.112) - Reply to #33

you mean tim willits. he is pretty clueless bout ql. so was hollenshead

syncerror call most of the shots thou.

syncerror call most of the shots thou.

Any game improvement on that update, or just the usual modifying non-game related stuff and passing that as patch notes?

Will it be their response to Reflex, or will it only consist of them trying to fix the bugs they introduced?

Will it be their response to Reflex, or will it only consist of them trying to fix the bugs they introduced?

Edited by megaman3 at 17:50 CST, 25 November 2014

damn you son.

What was wrote in op post? see dot

steam only release?

meh who care

qworld more fun

steam only release?

meh who care

qworld more fun

By Teen Queen

Keep on calling BS all you want, just remember how that turned out in this thread

By MajkiFajki - Reply to #27

That was super official - they had focus group and stuff.

There's still a focus group

Edited by sonic at 16:15 CST, 25 November 2014

By juan_juanson - Reply to #46

Well, Steam does have its own stats system, but I'm not too familiar with it. Some say it can provide better matchmaking. I think the comment about "no more ELO" was regarding third party stats sites.

By juan_juanson - Reply to #57

No idea how the matchmaking stuff is done by QL... They have a "skillrating" value assigned to players (which is related to tiers) but the formula used isn't really known. Steam's rating system is apparently ELO-based but it doesn't seem like they publicize ELO numbers.

As for QLRanks I think they're just using a spider bot to read the stats from the publicly available profile pages, but there might be more to it than that. With Steam exclusive, there wouldn't be any match results to crawl/index.

As for QLRanks I think they're just using a spider bot to read the stats from the publicly available profile pages, but there might be more to it than that. With Steam exclusive, there wouldn't be any match results to crawl/index.

Edited by agentsmith_ at 21:52 CST, 25 November 2014

QLranks and http://ql.leeto.fi/ use a simple streaming api Sponge wrote for them.

This means we can safely say that:

- QL has 3,000 players.

- CPM has 17 players.

- Warsow has more bots on servers than players.

- QL has 3,000 players.

- CPM has 17 players.

- Warsow has more bots on servers than players.

Yakumo:

Thank you, that is a new link I had not seen before.

While this counts matches, rather than number of players or number of subscribers, it is useful in spotting the overall trend.

The devs can use this chart to claim that all the changes leading up to the Steam release had a**net-positive** impact.

But at the same time we can see that the trend is downward, and in 2 months. This same chart will show a small net-loss.

Their 1Y subscription model means that there will also have been a small spike in subscriptions coinciding with the first few weeks of the Steam release....while the cancellations from the veterans will not show up until months later.

I guess for now the devs can hide behind these numbers inside Id.

But inside 6 months the ruse will be up. All numbers will be down, including revenue from subscriptions.

Thank you, that is a new link I had not seen before.

While this counts matches, rather than number of players or number of subscribers, it is useful in spotting the overall trend.

The devs can use this chart to claim that all the changes leading up to the Steam release had a

But at the same time we can see that the trend is downward, and in 2 months. This same chart will show a small net-loss.

Their 1Y subscription model means that there will also have been a small spike in subscriptions coinciding with the first few weeks of the Steam release....while the cancellations from the veterans will not show up until months later.

I guess for now the devs can hide behind these numbers inside Id.

But inside 6 months the ruse will be up. All numbers will be down, including revenue from subscriptions.

Edited by Norsak at 08:46 CST, 27 November 2014

By Anonymous (79.168.55.112) - Reply to #116

This is really good point. I think it will be very much down in 3 months already. bump when you see that

By Anonymous (95.141.28.120) - Reply to #34

By MarzenGold

I don't see how adding a dot is a big change.

I called bullshit on the other changes even after being assured they were real so I no longer trust my ability to predict the QL dev team. But at least the other leak had chat logs or whatever.

This is just a guy saying stuff.

Although by this point I've forgotten what the post initially said so I dont remember how realistic it could be

This is just a guy saying stuff.

Although by this point I've forgotten what the post initially said so I dont remember how realistic it could be

Things that devs talked about months ago.

Slowly planing to go steam only, along with some other consequences.

Slowly planing to go steam only, along with some other consequences.

By weltschmerz - Reply to #91

It's certainly within the realm of possibilities. Assumed the recent steam launch didn't bring the numbers the thing is now probably about to enter a major cost cutting stage (which in fact has been initiated already when dropping the linux/mac clients).

Don't know anything about steam, but the plan likely is to get rid of some of the costly infrastructure they're maintaining right now. Like stripping down the ql web site to a bare minimum, merely redirecting to somewhere else, would probably save them a noticeable amount of money already.

I mean, just recall how the thing started out. Back then Carmack seemed to hope he might be setting a trend with the ingame advertising and such. Never took off though, and ql now seems to be stuck in a dead end while not being really dead at the same time. But the chances of turning it into a cash cow again are practically zero, so from a business perspective the game presumably lost all its appeal.

Don't know anything about steam, but the plan likely is to get rid of some of the costly infrastructure they're maintaining right now. Like stripping down the ql web site to a bare minimum, merely redirecting to somewhere else, would probably save them a noticeable amount of money already.

I mean, just recall how the thing started out. Back then Carmack seemed to hope he might be setting a trend with the ingame advertising and such. Never took off though, and ql now seems to be stuck in a dead end while not being really dead at the same time. But the chances of turning it into a cash cow again are practically zero, so from a business perspective the game presumably lost all its appeal.

By juan_juanson - Reply to #99

The game continues to be a halo product for Id Software. They value the brand and its reputation, or they wouldn't host Quakecon every year or have kept QL running so long. Not that I disagree with your point about cost cutting, but I don't think the game not being a direct money maker means it has no business value/appeal to Id.

Edited by agentsmith_ at 16:22 CST, 26 November 2014

By weltschmerz - Reply to #106

Sure, that's what I used to be saying. Problem is though that id Software, or remains thereof, aren't free to operate anymore like they want. They're property of Zenimax, who likely paid a handsome sum for the company, and who by now very likely also subsidize id Software, because that branch might not be able to sustain its prolonged development efforts anymore all by itself.

So what I'm imagining is that at some point Zenimax might tell id to either produce something worthwhile or start cutting costs, to the point of even losing their diva status within the company and getting absorbed as just another development division amongst others.

So from a Willits and cohorts point of view, when that's about to happen the priority presumably is to get d4 done no matter what, also to prove that they're able to push something out with Carmack gone, and fuck ql if that proves to be a roadblock money wise. You know, in a do or die fashion.

And whether d4 is going to happen anytime soon when their big "reveal" at last qcon was just another trailer - about which those deplorable fuckers made tox wait for his last game of the day vs dahang - well, to be perfectly frank, I kind of doubt it.

So what I'm imagining is that at some point Zenimax might tell id to either produce something worthwhile or start cutting costs, to the point of even losing their diva status within the company and getting absorbed as just another development division amongst others.

So from a Willits and cohorts point of view, when that's about to happen the priority presumably is to get d4 done no matter what, also to prove that they're able to push something out with Carmack gone, and fuck ql if that proves to be a roadblock money wise. You know, in a do or die fashion.

And whether d4 is going to happen anytime soon when their big "reveal" at last qcon was just another trailer - about which those deplorable fuckers made tox wait for his last game of the day vs dahang - well, to be perfectly frank, I kind of doubt it.

By juan_juanson - Reply to #109

I don't disagree, but the cost of running QL (i.e. whatever the operating loss is) is probably minuscule compared to the company's other expenses/projects, like D4. So I'm not sure QL's operating loss would even be on the radar of top Zenimax execs. Agreed that D4 is probably 'do or die' for Id, outside of engine licensing.

Edited by agentsmith_ at 17:32 CST, 26 November 2014

Since the acquisition that id doesn't license their engines anymore, outside Zenimax.

I think it's quite obvious Zenimax bought id with the intent of having it as their engines supplier studio and of course being able to use their franchises. If id does poorly on doom4, just like it did with rage and doom3 (their only three main games in 15 year so far), then it will only continue to exist as a technical studio, not making games themselves anymore, and the next quake will be made by some related company like Raven Software, which isn't a bad thing at all tbh considering that since quake3 that external developers use id's engines and franchises way better than id itself.

I think it's quite obvious Zenimax bought id with the intent of having it as their engines supplier studio and of course being able to use their franchises. If id does poorly on doom4, just like it did with rage and doom3 (their only three main games in 15 year so far), then it will only continue to exist as a technical studio, not making games themselves anymore, and the next quake will be made by some related company like Raven Software, which isn't a bad thing at all tbh considering that since quake3 that external developers use id's engines and franchises way better than id itself.

By weltschmerz - Reply to #111

And in this spirit a best case scenario might be Zenimax actually trying to take ql out of id's hands in a gentle manner, without publicly humiliating and disgruntling them, and eventually do something better with it. Who knows, good things do occasionally happen.

By asdfasdfasdf - Reply to #115

quake mmo?

quake but at e-sports competition level of production as ie. stracraft, cs:go, dota2.

If that happens i would be so happy. This game needs a rescuer to get it going on a new level, but by that they need to re-brand it. Else you fuckers are just gona go ... meeeeh its not q3...

If that happens i would be so happy. This game needs a rescuer to get it going on a new level, but by that they need to re-brand it. Else you fuckers are just gona go ... meeeeh its not q3...

If it was .* then yes, it would. ( http://www.regular-expressions.info/dot.html )

By weltschmerz - Reply to #100

What I always meant to ask you, did all the effort you put into q4max ever pay off in one way or another?

not rly

As much as any other hobby gets you - gave me interesting challenges to solve and kept my interest for many months. It also sustained Q4 for a lot longer than it would have lasted for otherwise.

If you mean in terms of getting a job or something, I already had a perfectly good job, and wasn't looking to find a job in the games industry.

If you mean in terms of getting a job or something, I already had a perfectly good job, and wasn't looking to find a job in the games industry.

Edited by AnthonyJ at 16:01 CST, 27 November 2014

By weltschmerz - Reply to #126

Glad to hear there's no regrets. Because from my pov you guys were not only handed the shittiest engine of them all to work with (Carmack's reply to everything that was wrong with it: we leave that to the modders) but also fucked by id themselves when they nullified your work with the ql beta. But, as you said, there's certainly pride to take in keeping the thing afloat for longer than otherwise could have been expected.

By asdfasdfasdf - Reply to #124

and on the foot is the reality that . matches almost any character. regular expressions don't change anything.

I welcome our steam exclusive overlords. There is gonna be a whole lot of rage when all the wallers and aim assist kids can't win anymore.

I like how this thread suddenly condensed into a singularity "." and then burst into a supermassive weird-sequence hyperdense moronic twat cloud, enveloping everything in its path with a thick layer of pretentious wank, eventually decaying into nothing except for residual traces of background virginity radiation and broken netcode.

Edited by quake is potat at 06:20 CST, 28 November 2014

By Troll Rapist - Reply to #163

the internet means alot to you doesnt it?

By Anonymous (79.168.55.112) - Reply to #169

no, zenimax still think ql make profit

Sirax,

I haven't forgotten that your that your implementation of multiplayer ELO/Trueskill is tragically flawed. That you are too lazy to fix it, and that your response to criticism (but...but.. the document says TrueSkill is better) is about as clever as anything Syncerror has come up with this year.

You both deserver to become dusty footnotes in this final chapter of the Quake franchise.

I haven't forgotten that your that your implementation of multiplayer ELO/Trueskill is tragically flawed. That you are too lazy to fix it, and that your response to criticism (but...but.. the document says TrueSkill is better) is about as clever as anything Syncerror has come up with this year.

You both deserver to become dusty footnotes in this final chapter of the Quake franchise.

By weltschmerz - Reply to #177

"Final chapter" sounds like the beginning of something.

By weltschmerz - Reply to #180

Won't prevent you from taking one.

The argument I had with qlranks.com was not if Trueskill was better than Elo.

The argument was:**qlranks did not implement Trueskill correctly.**

But when challenged to explain how players can loose points on Qlranks while winning a game, the response was: Trueskill is better than Elo !!

So I'm lumping sirax in with syncerror: Too arrogant to admit when they are wrong, not smart enough to fix their own mistakes.

The argument was:

But when challenged to explain how players can loose points on Qlranks while winning a game, the response was: Trueskill is better than Elo !!

So I'm lumping sirax in with syncerror: Too arrogant to admit when they are wrong, not smart enough to fix their own mistakes.

But when challenged to explain how players can loose points on Qlranks while winning a game, the response was: Trueskill is better than Elo !!I literally quoted the parts of the paper that explain how that can happen.

The multiplayer part is flawed, duel works just fine.

Turns out Trueskill is really really complex, and very difficult to fully understand and codify.

I don't buy for 1sec that either you or sirax cracked that nut.

(evidenced by the fact that you use an Elo scale while claiming to use Trueskill, and that** THERE IS NO SET OF CIRCUMSTANCES in Trueskill where the winning player can loose score or Ranking.)**

But since you are arrogant SOBs, you couldn't admit that your multiplayer code is neither Elo nor Trueskill, and that it's not perfect.

Instead you simply claimed that you used Trueskill and pretended the agument was about the merits of Trueskill.

Turns out Trueskill is really really complex, and very difficult to fully understand and codify.

I don't buy for 1sec that either you or sirax cracked that nut.

(evidenced by the fact that you use an Elo scale while claiming to use Trueskill, and that

But since you are arrogant SOBs, you couldn't admit that your multiplayer code is neither Elo nor Trueskill, and that it's not perfect.

Instead you simply claimed that you used Trueskill and pretended the agument was about the merits of Trueskill.

Edited by Norsak at 19:56 CST, 28 November 2014

THERE IS NO SET OF CIRCUMSTANCES in Trueskill where the winning player can loose score or RankingYes there is, I quoted the exact part of the paper that explains how it can happen.

But since you are arrogant SOBs, you couldn't admit that your multiplayer code is neither Elo nor Trueskill, and that it's not perfect.First of all, I have nothing to do with QLRanks. I asked Sirax after your last thread and he said they do use TrueSkill, so you're just wrong about that.

Edit: Here you go, I went to the trouble of finding it again:

The TrueSkill skill of a player i is currently displayed as a conservative skill estimate given by the 1% lower quantile mu_i - 3*sigma_i. This choice ensures that the top of the leaderboards (a listing of all players according to mu - 3*sigma) are only populated by players that are highly skilled with high certainty, having worked up their way from 0 = mu_0 - 3*sigma_0.

...

If the skills are expected to vary over time, a Gaussian dynamics factor N (s_{i;t+1}; s_{i;t}; gamma^2) can be introduced which leads to an additive variance component of gamma^2 in the subsequent prior.

Edited by obi at 20:11 CST, 28 November 2014

By asdfasdfasdf - Reply to #187

you mean 0* = mu_0* - 3*sigma_0*, right?

Edited by Gobotz at 21:47 CST, 28 November 2014

Edit: Here you go, I went to the trouble of finding it again:

The TrueSkill skill of a player i is currently displayed as a conservative skill estimate given by the 1% lower quantile mu_i - 3*sigma_i. This choice ensures that the top of the leaderboards (a listing of all players according to mu - 3*sigma) are only populated by players that are highly skilled with high certainty, having worked up their way from 0 = mu_0 - 3*sigma_0.

...

If the skills are expected to vary over time, a Gaussian dynamics factor N (s_{i;t+1}; s_{i;t}; gamma^2) can be introduced which leads to an additive variance component of gamma^2 in the subsequent prior.

Yes, I remember.

And that doesn't mean shit to you, because you can not re-phrase that. It also says nothing that in anyway explains how winning can equal a loss of ranking.

Of course I can rephrase it, but surely a direct quote from the paper is better than hearing it filtered through me?

The system maintains a belief about player skill, represented by a probability distribution over all possible ratings. In order to condense this to a single value they use mu - 3*sigma, where mu is the mean and sigma is the standard deviation of the distribution. This is because it is more stable than the mean - it represents a lower bound on a players skill with 99% confidence.

As you play more games, it gets more confident in your skill estimate, so your standard deviation is lowered. This makes is difficult to raise your rating if you improve, so they make your standard deviation bigger before each calculation to compensate.

If you play a game that was too poorly matched, your true estimate (the mean) goes up by less than the additive factor on your standard deviation. So your displayed rating can go down.

The system maintains a belief about player skill, represented by a probability distribution over all possible ratings. In order to condense this to a single value they use mu - 3*sigma, where mu is the mean and sigma is the standard deviation of the distribution. This is because it is more stable than the mean - it represents a lower bound on a players skill with 99% confidence.

As you play more games, it gets more confident in your skill estimate, so your standard deviation is lowered. This makes is difficult to raise your rating if you improve, so they make your standard deviation bigger before each calculation to compensate.

If you play a game that was too poorly matched, your true estimate (the mean) goes up by less than the additive factor on your standard deviation. So your displayed rating can go down.

Edited by obi at 20:39 CST, 28 November 2014

Yes there is, I quoted the exact part of the paper that explains how it can happen.

No you didn't. You tried to pull a fast one, you copied bits and pieces that sounded good.

Honestly: I do not believe that you personally have a detailed understanding of Trueskill.

I asked Sirax after your last thread and he said they do use TrueSkilCorrect, and I claim that sirax lied to you.

Sirax is an arrogant SOB, because instead of fixing his broken code he claims to be using Trueskill, and pretending this nullifies all follow-up questions.

You (obi) are an SOB because you are pretending that you know more about Trueskill than you do, and decided to blindly go to bat for sirax instead of examining the evidence.

What I posted explains exactly how you can lose rating points. Maybe try reading and understanding the paper before raging at people?

You made a statement and were shown to be incorrect. So now you just accuse people of lying because you can't understand what was given to you.

Honestly: I do not believe that you personally have a detailed understanding of Trueskill.Well I actually went and read the paper. Have you tried that? What kind of way is this to argue?

You made a statement and were shown to be incorrect. So now you just accuse people of lying because you can't understand what was given to you.

Obi: you are a bullshit artist.

If you understood Trueskill as well as you claim, you could expand on the subject matter, you could structure an argument that little old me could understand. Instead all you are doing is pointing at 'The paper' and at the snipet to re-posted above.

Those are not the tell tall signs of someone who has mastered the subject as you claim.

If you understood Trueskill as well as you claim, you could expand on the subject matter, you could structure an argument that little old me could understand. Instead all you are doing is pointing at 'The paper' and at the snipet to re-posted above.

Those are not the tell tall signs of someone who has mastered the subject as you claim.

Edited by Norsak at 20:40 CST, 28 November 2014

I have never claimed to have "mastered" anything and I gave you a full explanation above. Hopefully you will respond to it.

Should I draw you a fucking picture as well?

Should I draw you a fucking picture as well?

Edited by obi at 20:41 CST, 28 November 2014

Should I draw you a fucking picture as well?

I challenge you to do so.

For anyone who happens to be reading along, here is a link to "The Paper" that obi claims he has read link

The reason I don't believe him is simple: You can't actually read that paper. What you can try to do in work through it methodically. I tried and gave up after a few days when it became evident that there was not enough detail in that paper to obtain a full understanding of the algorithms needed to implement Trueskill !

So I stand by my claim: Obi is full of shit. Sirax is full of shit

Obi is trying use a playground bluff, where he makes fun of you for not knowing the word "queef". He doesn't know what it means either. He just keeps saying: "If you don't know I'm not gonna tell you..."

So now you are just going to ignore what I wrote above? I have already given you the explanation.

Here it is again:

Here it is again:

The system maintains a belief about player skill, represented by a probability distribution over all possible ratings. In order to condense this to a single value they use mu - 3*sigma, where mu is the mean and sigma is the standard deviation of the distribution. This is because it is more stable than the mean - it represents a lower bound on a players skill with 99% confidence.

As you play more games, it gets more confident in your skill estimate, so your standard deviation is lowered. This makes is difficult to raise your rating if you improve, so they make your standard deviation bigger before each calculation to compensate.

If you play a game that was too poorly matched, your true estimate (the mean) goes up by less than the additive factor on your standard deviation. So your displayed rating can go down.

Here is what he means with a simple example :

Estimate = mean - 3*standardDeviation

BEFORE the match:

mean : 0

standard deviation : 1

estimate = 0 - 3*1 = -3

Result of the match :

mean increased by 1 (it was a victory)

standard deviation increased by 0.5 (poor match)

AFTER the match :

mean : 1

standard deviation : 1.5

estimate = 1 - 3*1.5 = -3.5

Don't take it as a precise example of a situation that could happen with those exact values. It's just there so you can grasp the concept of how a victory can decrease the estimate.

Estimate = mean - 3*standardDeviation

BEFORE the match:

mean : 0

standard deviation : 1

estimate = 0 - 3*1 = -3

Result of the match :

mean increased by 1 (it was a victory)

standard deviation increased by 0.5 (poor match)

AFTER the match :

mean : 1

standard deviation : 1.5

estimate = 1 - 3*1.5 = -3.5

Don't take it as a precise example of a situation that could happen with those exact values. It's just there so you can grasp the concept of how a victory can decrease the estimate.

Edited by FlashSoul at 21:27 CST, 28 November 2014

FlashSoul,

I admit that I don't have a full grasp on th Trueskill algorithm, but it's a little more complicated than what you have sketched out.

I did a little research when i still cared about QL, and I could only find one person who actually worked it all out and published the details:Jeff Moser

That guy is way smarter that any of us (including sirax), and he actually codified his finding in an on-line simulator: link

Try it, you can tweak Mu (mean) and sigma (standard deviation) any way you like, the winner CAN NOT loose ranking.

Go ahead plug in mean=0, Standard deviation=1

Now if you want to argue that your above sketch trumps Jeff Moser, fair enough.

I admit that I don't have a full grasp on th Trueskill algorithm, but it's a little more complicated than what you have sketched out.

I did a little research when i still cared about QL, and I could only find one person who actually worked it all out and published the details:Jeff Moser

That guy is way smarter that any of us (including sirax), and he actually codified his finding in an on-line simulator: link

Try it, you can tweak Mu (mean) and sigma (standard deviation) any way you like, the winner CAN NOT loose ranking.

Go ahead plug in mean=0, Standard deviation=1

Now if you want to argue that your above sketch trumps Jeff Moser, fair enough.

Edited by Norsak at 22:01 CST, 28 November 2014

I got it to show the winner losing ranking no problem. Just make the teams very unbalanced and use a small sigma value....

Here's a quote from your hero Jeff Moser's blog:

Are you done calling people liars yet?

Here's a quote from your hero Jeff Moser's blog:

One surprising thing is that if you have a really low standard deviation and play a game that has very bad match quality (see my accompanying paper for details but this usually means a very unfair match), it could be that your TrueSkill goes down after a win.http://www.moserware.com/2010/03/computing-your-skill.html

Are you done calling people liars yet?

Edited by obi at 22:21 CST, 28 November 2014

I'm not gonna plug mean=0, sd =1 because, as I specified in the previous post, those values were not meant to be taken like that. I will comply with your little test though.

https://dl.dropboxusercontent.com/u/74076095/oops.png

Alice before her victory : 24.011

Alice after her victory : 23.971

Try it, you can tweak Mu (mean) and sigma (standard deviation) any way you like, the winner CAN NOT loose ranking.

https://dl.dropboxusercontent.com/u/74076095/oops.png

Alice before her victory : 24.011

Alice after her victory : 23.971

Edited by FlashSoul at 22:35 CST, 28 November 2014

By Anonymous (77.108.65.195) - Reply to #204

your picture shows smth quite opposite to what you claim here

It doesn't.

Alice before her victory : 25 - 3*0.333 = 24.011

Alice after her victory : 25 - 3*0.343 = 23.971

Therefor, Alice's conservative skill estimate decreased after her victory.

If you still disagree about something there, please elaborate so I can actually understand what I should explain better. I genuinely don't know what you disagree with exactly so it's kinda hard to refute it.

Alice before her victory : 25 - 3*0.333 = 24.011

Alice after her victory : 25 - 3*0.343 = 23.971

Therefor, Alice's conservative skill estimate decreased after her victory.

If you still disagree about something there, please elaborate so I can actually understand what I should explain better. I genuinely don't know what you disagree with exactly so it's kinda hard to refute it.

quakelivelauncher on linux by FX works really good too :'(

best solution ever.

dump QL...

re-release q3 with the server browser and that shit from QL.

charge a one time fee.

let people run their own servers.

we can play all the mods and maps forever and ever.

instead of the company having to dump money into a project that makes no money....

now they wont have to. everyone wins.

dump QL...

re-release q3 with the server browser and that shit from QL.

charge a one time fee.

let people run their own servers.

we can play all the mods and maps forever and ever.

instead of the company having to dump money into a project that makes no money....

now they wont have to. everyone wins.

Pastebin etc or any other place where this information is posted?

What I'm gathering from the comments:

1. Steam only to employ the use of VAC.

2. Cease and desist for qlranks inbound, presumably using a steam skillrating system or the removal of any such system from the game?

3. ...?

Also, a big thanks to all the folks devoting their resources to their qlranks system (sirax, szr and several more) and their qlranks stream. This group of folks have built an informative and useful system, built in their spare time, that put the official "skill rating" system to absolute shame (admittedly not particularly hard) of which players were/are paying to get there in-game experiences ruined by.

The entire quake live project is just an absolute massive waste of wonderful potential for our beloved genre and genesis of online shooter, of which I hope reflex and others can fill and this game can thankfully be put aside and long forgotten.

Doesn't matter whose fault it is, be it id/bethesda not supplying sufficient resources to the ql team, or the poor use of resources by the ql team itself; still a giant waste, great shame and shadow of what could have been.

What I'm gathering from the comments:

1. Steam only to employ the use of VAC.

2. Cease and desist for qlranks inbound, presumably using a steam skillrating system or the removal of any such system from the game?

3. ...?

Also, a big thanks to all the folks devoting their resources to their qlranks system (sirax, szr and several more) and their qlranks stream. This group of folks have built an informative and useful system, built in their spare time, that put the official "skill rating" system to absolute shame (admittedly not particularly hard) of which players were/are paying to get there in-game experiences ruined by.

The entire quake live project is just an absolute massive waste of wonderful potential for our beloved genre and genesis of online shooter, of which I hope reflex and others can fill and this game can thankfully be put aside and long forgotten.

Doesn't matter whose fault it is, be it id/bethesda not supplying sufficient resources to the ql team, or the poor use of resources by the ql team itself; still a giant waste, great shame and shadow of what could have been.

By asdfasdfasdf

Edited by brandan at 02:06 CST, 30 November 2014

I AM OFFENDED AND BULLIED BY THIS POST

btw... perhaps you should also add in the first 10 posts which were before that in which I fairly politely re-explained something to the same person who I already explained the same thing to a year ago.

Most esr users would've told him to fuck off and kill himself. I tried to help the confused kid.

Perhaps it would've been better if I told him to fuck off and kill himself though.

Most esr users would've told him to fuck off and kill himself. I tried to help the confused kid.

Perhaps it would've been better if I told him to fuck off and kill himself though.

Good job. You've unsuccessfully rid the world of stupidity that you and your college club has exclusive rights to be burdened by. So terrible for you to be forced to educate and bear with these "soft" dimwitted chimps on the internet who can't appreciate your perspectives. Jeeze you're breaking our hearts here.

By asdfasdfasdf - Reply to #303

i understand that it can be painful and difficult to accept unsavory facts about ourselves, but if we are not honest and objective with our understanding of ourselves, then how can we ever progress, or even be satisfied that we have even attempted to penetrate the delusional fog of our personal desires?

i believe that you possess the mental fortitude to overcome this, weird.

i believe that you possess the mental fortitude to overcome this, weird.

Edited by brandan at 19:36 CST, 30 November 2014

unsavory facts about myself?

I don't see anything unsavory about what you posted other than that it lacks context.

The context being that if they treat me as if I'm some kind of braindead idiot while meanwhile not actually reading what I say, then after a few posts they lose their value as equals (where everyone starts out) and attain the value of garbage.

I don't treat my garbage with any respect either.

This doesn't mean that I am a bully because bullies treat everyone as garbage. Aka everyone starts out like garbage if you're a bully.

I don't need to "be nice to everyone" :)

I don't see anything unsavory about what you posted other than that it lacks context.

The context being that if they treat me as if I'm some kind of braindead idiot while meanwhile not actually reading what I say, then after a few posts they lose their value as equals (where everyone starts out) and attain the value of garbage.

I don't treat my garbage with any respect either.

This doesn't mean that I am a bully because bullies treat everyone as garbage. Aka everyone starts out like garbage if you're a bully.

I don't need to "be nice to everyone" :)

By asdfasdfasdf - Reply to #326

a few posts before you said:

*Look here....*

I've been pretty polite up till now and I'd like to keep it that way.

you called obi an idiot. you are in denial about your abusive behavior. bullies justify their abuse by dehumanizing their victims, such as your equation of your victims to garbage.

you attempt to regress from the realization that you are a bully by applying arbitrary and irrelevant terms and conditions to the definition of bully. this is not how language works.

*intellectual: appealing to or engaging the intellect*

bully: a blustering, quarrelsome, overbearing person who habitually badgers and intimidates smaller or weaker people.

you use abusive language to intimidate people you consider lesser than you when it comes to intellectual matters. you are an intellectual bully. there are multiple demonstrations of this behavior in this thread. there is one example of it in this post.

your understanding of the sequence of events in this thread is clouded by your desires. this post demonstrates one example of your tendency to be abusive in arguments, and your confusing forgetfulness about that abuse (claiming you have been polite in a discussion, when you have previously, in the same discussion, been insulting).

i hope that this is not a sickness, weird. it would be a shameful waste of intelligence for you to be mentally ill.

I've been pretty polite up till now and I'd like to keep it that way.

you called obi an idiot. you are in denial about your abusive behavior. bullies justify their abuse by dehumanizing their victims, such as your equation of your victims to garbage.

you attempt to regress from the realization that you are a bully by applying arbitrary and irrelevant terms and conditions to the definition of bully. this is not how language works.

bully: a blustering, quarrelsome, overbearing person who habitually badgers and intimidates smaller or weaker people.

you use abusive language to intimidate people you consider lesser than you when it comes to intellectual matters. you are an intellectual bully. there are multiple demonstrations of this behavior in this thread. there is one example of it in this post.

your understanding of the sequence of events in this thread is clouded by your desires. this post demonstrates one example of your tendency to be abusive in arguments, and your confusing forgetfulness about that abuse (claiming you have been polite in a discussion, when you have previously, in the same discussion, been insulting).

i hope that this is not a sickness, weird. it would be a shameful waste of intelligence for you to be mentally ill.

Edited by brandan at 20:10 CST, 30 November 2014

Did I not get much more impolite after that post?

I said I was pretty polite before... I didn't say I was incredibly polite.

For esr standards I was pretty polite imo ;)

I dunno about you but in my eyes bullies take action (out of themselves) against people because they view them as weak.

They seek out those less fortunate then themselves and bully them around.

I don't seek out people. People enter into a debate with me. As long as they are presenting arguments than I have np countering those. But as soon as they will just re-iterate their own beliefs and misinterpret/twist my words then I find that insulting towards myself.

Shortly after such things happen I think that it's ok for me to insult them back. During this thread I even said that I felt insulted by his questions and urged him not to tempt me :)

That he does so regardless of my warning is completely up to him.

If your only idea that 'I started bullying' is comment 141 then you should realize that it is a reference to the thread of last year. Where I had already made certain that they (the 2 idiots) were not attempting to debate anything they were simply too stupid to understand the concept. (Which in my book makes them idiots as they think they present arguments while they do not understand the basics of what they are arguing against)

I guess that would clear up all issues you might have :D

If you still have other issues then lemme know.

I said I was pretty polite before... I didn't say I was incredibly polite.

For esr standards I was pretty polite imo ;)

I dunno about you but in my eyes bullies take action (out of themselves) against people because they view them as weak.

They seek out those less fortunate then themselves and bully them around.

I don't seek out people. People enter into a debate with me. As long as they are presenting arguments than I have np countering those. But as soon as they will just re-iterate their own beliefs and misinterpret/twist my words then I find that insulting towards myself.

Shortly after such things happen I think that it's ok for me to insult them back. During this thread I even said that I felt insulted by his questions and urged him not to tempt me :)

That he does so regardless of my warning is completely up to him.

If your only idea that 'I started bullying' is comment 141 then you should realize that it is a reference to the thread of last year. Where I had already made certain that they (the 2 idiots) were not attempting to debate anything they were simply too stupid to understand the concept. (Which in my book makes them idiots as they think they present arguments while they do not understand the basics of what they are arguing against)

I guess that would clear up all issues you might have :D

If you still have other issues then lemme know.

By asdfasdfasdf - Reply to #329

i feel that, in time, as your meaningful and interesting thoughts are ignored and ridiculed by the community, that you will begin to understand your position. i hope that when that understanding begins, you will think back to this conversation and have an anchor point from which to begin to achieve what you are capable of.

is that what you feel has happened to you?

(btw I already understand the position you are refering to...

Because ever since trying to explain my completely justifiable whine on netcode. The community seems to think that I have tried to make excuses for being not better than sponsored pro's at a game.

These factually correct meaningful and interesting thoughts have been ignored and ridiculed by the community.

Although I should possibly add that in recent months / a year or so the view of the community is slowly changing from "roflmao that is some ridiculous way to come up with an excuse hahah omfg" to "Omfg the guy was right. But let's not admit it.")

(btw I already understand the position you are refering to...

Because ever since trying to explain my completely justifiable whine on netcode. The community seems to think that I have tried to make excuses for being not better than sponsored pro's at a game.

These factually correct meaningful and interesting thoughts have been ignored and ridiculed by the community.

Although I should possibly add that in recent months / a year or so the view of the community is slowly changing from "roflmao that is some ridiculous way to come up with an excuse hahah omfg" to "Omfg the guy was right. But let's not admit it.")

By asdfasdfasdf - Reply to #331

i don't think that is what has happened to me. would you feel better about this if you were not alone in it?

also, i was referring to your thoughts on the philosophical conceptualization of infinity. it's fascinating, and it's important, for progress of knowledge, that people pioneer thinking outside the frontiers of established practices. but it's good to know that you are aware of this pattern of social rejection.

also, i was referring to your thoughts on the philosophical conceptualization of infinity. it's fascinating, and it's important, for progress of knowledge, that people pioneer thinking outside the frontiers of established practices. but it's good to know that you are aware of this pattern of social rejection.

First of all I don't mind being alone in things. It's challenging and I like a good challenge :D

I asked it because you are often being ridiculed by this community however upon further inquiry you actually do seem to know what you are talking about.

So I was wondering if you would view yourself as being in this position ;)

Partially because you seem to find it important to find fault in others (in this case me, but in other cases other people)... This would seem to indicate some sort of frustration which may be similar to my own when people refuse to think yet beg to differ ;)

I asked it because you are often being ridiculed by this community however upon further inquiry you actually do seem to know what you are talking about.

So I was wondering if you would view yourself as being in this position ;)

Partially because you seem to find it important to find fault in others (in this case me, but in other cases other people)... This would seem to indicate some sort of frustration which may be similar to my own when people refuse to think yet beg to differ ;)

By asdfasdfasdf - Reply to #333

for those who desire and value loneliness (or: uniqueness), it is easy to maintain that loneliness by lending to the social perception of your own unique thoughts and ideas as unsavory with simple behavioral tactics, such as abusive bullying. it is not difficult to vilify yourself to others this way, and it follows that your thoughts and ideas will assume the taint of your vilification in the eyes of others.

from this basic assumption, we can conclude that you are worried that others will discover that you are truly not such a bully as you would like to appear, and so you fight against my accusation to appear not to be a bully, as the defensive stance is a common indicator of guilt, because were others to discover your humble nature they would more readily embrace your ideas, and your way of thinking would become less unique, and your value thereby diminished through the process of ideological dilution by social conception.

it's really brilliant reverse psychology, weird, but it is now exposed for all. and i have faith that everybody here can see your desperate attempts at character assassination for what they are.

from this basic assumption, we can conclude that you are worried that others will discover that you are truly not such a bully as you would like to appear, and so you fight against my accusation to appear not to be a bully, as the defensive stance is a common indicator of guilt, because were others to discover your humble nature they would more readily embrace your ideas, and your way of thinking would become less unique, and your value thereby diminished through the process of ideological dilution by social conception.

it's really brilliant reverse psychology, weird, but it is now exposed for all. and i have faith that everybody here can see your desperate attempts at character assassination for what they are.

I'm getting too close to you huh?

Shame ;(

Anyways I don't value uniqueness... Nor do I try to portray my thoughts as being unsavory.

If anything I would try to spread my "unique thoughts". (although in this thread my thoughts aren't very unique as similar thoughts are in the work of Euler and Newton... 2 people who did amazing things)

But anyway, the post wasn't about me... I think it was about you...

How come you are 'wasting your time' on esr?

Shame ;(

Anyways I don't value uniqueness... Nor do I try to portray my thoughts as being unsavory.

If anything I would try to spread my "unique thoughts". (although in this thread my thoughts aren't very unique as similar thoughts are in the work of Euler and Newton... 2 people who did amazing things)

But anyway, the post wasn't about me... I think it was about you...

How come you are 'wasting your time' on esr?

By asdfasdfasdf - Reply to #335

so then what you are saying is that i am not correct in my recent assumption that you are not actually an intellectual bully?

and here you admit that you don't even have to*try* to be unsavory. i think there isn't much left to say.

and here you admit that you don't even have to

Your problem is that you see being polite as some sort of accomplishment, instead of the default way in which normal people communicate. How you act is your responsibility, not mine, and putting conditions on your politeness is just trying to deflect responsibility for being an asshole to people.

It way my fault Brandan, I... I asked him too many questions. I know he loves me really.

I can change him.

I can change him.

Edited by obi at 10:40 CST, 1 December 2014

By acid_reptile

What is this thread about and why got the first post deleted?

It's one of the longest "is 0.99 really 1?" debates in history of mankind, in a thread about QL going steam only.

That's ESR for you.

That's ESR for you.

So it was about leaked information? Don't see why it got deleted. How many times a QL changelog have been leaked before.. Someone has a screenshot PM me :d

It was never deleted and wasn't really a "leak" since devs talked about this publicly.

OP decided to pull a walter and replace the content with a dot, however none of the admins touched the thread so far.

OP decided to pull a walter and replace the content with a dot, however none of the admins touched the thread so far.

Alright. Tried to read the thread and gave up really quick. Its just 3 people posting OT stuff again and again . Found my info anyways http://webcache.googleusercontent.com/search?...=firefox-a

Thanks.

Thanks.

So i can use custom pk3's to get red hitsparks for example? Nice.

pffft. i doubt that. lol

i meant no stats and aliasing from one account.

but i would say...

look at the direction ql is going...

do you think it's actually going to get better?

I see it getting worse.

if you think the game has been noobed out...

the next release will probably be even noobier.

well probably have aim assist and locators.

I have absolutely no hope for quake.

i meant no stats and aliasing from one account.

but i would say...

look at the direction ql is going...

do you think it's actually going to get better?

I see it getting worse.

if you think the game has been noobed out...

the next release will probably be even noobier.

well probably have aim assist and locators.

I have absolutely no hope for quake.

This thread is about having an intervention for weird because he is an abusive father.

Weird, did you create this? http://whyevolutionistrue.wordpress.com/2013/...square-go/

not sure why you're pointing at me?

Moron1 claims that there is a difference... To whom I say that if you want to express the difference that you need infinitesimals.

At which point moron2 points to the hyperreals and claims that I'm wrong (while this system includes infinitesimals).

The difference between the 2 systems is pretty much exactly this (in one 0.999 = 1 by definition, in the other there is an infinitesimal difference and the proof of equality takes a lot more work... and depending on how you deal with concepts of infinity this may not even be possible), and they are not equal systems.

While moron2 seems to think that these systems are actually interchangeable moron1 doesn't understand the system at all.

ninja edit: I do not consider myself to be one of the 2 morons ;)

Moron1 claims that there is a difference... To whom I say that if you want to express the difference that you need infinitesimals.

At which point moron2 points to the hyperreals and claims that I'm wrong (while this system includes infinitesimals).

The difference between the 2 systems is pretty much exactly this (in one 0.999 = 1 by definition, in the other there is an infinitesimal difference and the proof of equality takes a lot more work... and depending on how you deal with concepts of infinity this may not even be possible), and they are not equal systems.

While moron2 seems to think that these systems are actually interchangeable moron1 doesn't understand the system at all.

ninja edit: I do not consider myself to be one of the 2 morons ;)

Edited by Weird at 09:12 CST, 1 December 2014

At which point moron2 points to the hyperreals and claims that I'm wrong (while this system includes infinitesimals).The hyper reals have infinitesmals, but not they don't allow you to divide by zero which is what I was arguing.

I'll try to be careful here and not phrase anything in the form of a question.

I answered this on Comment #287 @ 18:03 CET, 18 March 2013

Which is the first(!) ever notion I make of 0*.

Which I do on your request because you were whining that 0 has different properties in the system that I used to explain to you the concept of an infinitesimal.

Therefor I HAD ALREADY ANSWERED THIS BEFORE YOU ASKED.

I clearly state that if you would like to introduce 0* in a model where 0 is an infinitesimal:

Even that x/0* is undefined. (Which is something I dislike)

Which is the first(!) ever notion I make of 0*.

Which I do on your request because you were whining that 0 has different properties in the system that I used to explain to you the concept of an infinitesimal.

Therefor I HAD ALREADY ANSWERED THIS BEFORE YOU ASKED.

I clearly state that if you would like to introduce 0* in a model where 0 is an infinitesimal:

Even that x/0* is undefined. (Which is something I dislike)

there never was an argument?

You asked back in 2013 if I could bring back your 0 by which you cannot divide and I said sure define it as 0* = 0 - 0 in my model.

There NEVER was a question... Did it really take you a full year to discover that you cannot read (which I also already pointed out to you in 2013)

Comment #333 @ 19:08 CET, 19 March 2013

clearly you haven't read how I defined 0* yet you think you know all about it... story of this thread innit.... people not reading me but then asking all sorts of irrelevant questions.

You asked back in 2013 if I could bring back your 0 by which you cannot divide and I said sure define it as 0* = 0 - 0 in my model.

There NEVER was a question... Did it really take you a full year to discover that you cannot read (which I also already pointed out to you in 2013)

Comment #333 @ 19:08 CET, 19 March 2013

clearly you haven't read how I defined 0* yet you think you know all about it... story of this thread innit.... people not reading me but then asking all sorts of irrelevant questions.

By asdfasdfasdf - Reply to #339

it's a lifestyle.

By asdfasdfasdf - Reply to #350

weird <333... brandan

weird is normal

brandan is strange (much pscychology, this is game site no?)

new update is nighttime but is end of development of game

ahha

brandan is strange (much pscychology, this is game site no?)

new update is nighttime but is end of development of game

ahha

By Anonymous (72.202.204.174) - Reply to #351

weird is normal, brandan is weird?

1/3 of the game will change.

:)

That's 0.333 for you

:)

That's 0.333 for you

By generic nickname - Reply to #389

the loadouts happened "surely it's nonsense ? they wouldn't do that, come on..."

now, anything goes concerning quakelive "updates"

now, anything goes concerning quakelive "updates"

By generic nickname - Reply to #391

tldr : mathematicians are mean

By wrong person - Reply to #391

tldr: weird - not a bully

"It's one of the longest "is 0.99 really 1?" debates in history of mankind, in a thread about QL going steam only.

That's ESR for you. "

That's ESR for you. "

Edited by quake is potat at 04:09 CST, 2 December 2014

Don't know what you mean. i did not judge anyone here. What i meant by fascinating, is the idea, that mathematics is not as clear cut as i made it out to be, but that it allows for creative and philosophical extensions which lead to different approaches and interpretations. The fun part is all of you arguing the one truth and then going mad throwing insults at each other.

You're thinking about algebra with real numbers.

That is very well defined.

Math itself is not just algebra though. It is much better to think about math as a way of prove based reasoning within philosophy.

Where you take a certain few axioms for granted (which are philosophical ones) and you reason this through proving that you will never reach any contradiction.

That is very well defined.

Math itself is not just algebra though. It is much better to think about math as a way of prove based reasoning within philosophy.

Where you take a certain few axioms for granted (which are philosophical ones) and you reason this through proving that you will never reach any contradiction.

Edited by Weird at 14:38 CST, 2 December 2014

By Teen Queen

<@sponge> there will def be stats still, dunno if there will be a way for third parties to access it

<@sponge> in a theoretical steam exclusive version quakelive.com goes away and all the ui is stored inside the game

and new maps + 1 returning bitter embrace, castle deathstalker, death or glory, drun mummy, industrial revolution, ragnarok, refinery, satanic, solarium, sorrow

<@sponge> in a theoretical steam exclusive version quakelive.com goes away and all the ui is stored inside the game

and new maps + 1 returning bitter embrace, castle deathstalker, death or glory, drun mummy, industrial revolution, ragnarok, refinery, satanic, solarium, sorrow

Yea but 1 = 0.999... and 0.999... does not exist. Therefore, no returning maps for you.

By generic nickname - Reply to #512

hey, thanks for that. I don't hang around on irc at all so any "insider knowledge" is welcome

You mean QL going Steam exclusive? Quite a few people, apparently.

https://www.esreality.com/post/2662856/quakelive-steam-and-vac/

https://www.esreality.com/post/2662856/quakelive-steam-and-vac/

The question is when really. If they keep on releasing 3 maps every 3 months all that list is fruitless.

[nemecel]Plus the usual complain that in all this time they didn't release a meaningful update or patch, like improving graphics and whatnot, but instead they pretty much charge for access to RA3 maps.[/nemecel]

[nemecel]Plus the usual complain that in all this time they didn't release a meaningful update or patch, like improving graphics and whatnot, but instead they pretty much charge for access to RA3 maps.[/nemecel]

Edited by asyyy at 14:16 CST, 3 December 2014

By weltschmerz - Reply to #552

Over? Analysis I prep course hasn't even begun yet.

Warmup exercise: if I defined "being able to get arbitrarily close to infinity" as the ability to get past any given positive number, would that definition make sense? If so, why. If not, why not.

Warmup exercise: if I defined "being able to get arbitrarily close to infinity" as the ability to get past any given positive number, would that definition make sense? If so, why. If not, why not.

By weltschmerz - Reply to #556

Heidelberg.

Seeing the (understandable) reluctance, these are the followup questions I would insist on having answered before saying anything. In the absence of a lawyer I mean.

* What set of numbers am I talking about

* what's the definition of "getting past" a number here

* what's the definition of infinity here

* what's the definition of "getting close" here.

Answers:

* natural numbers

* counting to a natural number greater the given one

* cardinality of the set of natural numbers

* with the previous answer in mind, that's basically the question.

Seeing the (understandable) reluctance, these are the followup questions I would insist on having answered before saying anything. In the absence of a lawyer I mean.

* What set of numbers am I talking about

* what's the definition of "getting past" a number here

* what's the definition of infinity here

* what's the definition of "getting close" here.

Answers:

* natural numbers

* counting to a natural number greater the given one

* cardinality of the set of natural numbers

* with the previous answer in mind, that's basically the question.

Edited by PredatH0r at 08:02 CST, 4 December 2014

ask Obi... he brought it up... 2ce....

I just find it an interresting topic :)

I don't seem to find it that interresting that I seek out others to discuss this with though... Just if it happens to cross my path I'll shine a light on it.

I do sometimes bring up prime numbers on a more math related forum. As I wrote my own prime number calculator which works very different from others.... Although it looks a bit like a sieve ;)

I just find it an interresting topic :)

I don't seem to find it that interresting that I seek out others to discuss this with though... Just if it happens to cross my path I'll shine a light on it.

I do sometimes bring up prime numbers on a more math related forum. As I wrote my own prime number calculator which works very different from others.... Although it looks a bit like a sieve ;)

it works like this.

You first ask me a stupid question.

I tell you the answer to that stupid question.

You then tell my you don't comprehend my answer.

Which leads to me explaining my answer.

Which leads to you not understanding but rephrasing the stupid question as a followup question.

Which leads to me re-explaining my answer.

Which leads to you starting to trolll.

Which leads to me getting frustrated.

Which leads to even more stupid shit from your side.

Which leads to me getting kinda angry.

Which leads to me insulting your braindead head.

You first ask me a stupid question.

I tell you the answer to that stupid question.

You then tell my you don't comprehend my answer.

Which leads to me explaining my answer.

Which leads to you not understanding but rephrasing the stupid question as a followup question.

Which leads to me re-explaining my answer.

Which leads to you starting to trolll.

Which leads to me getting frustrated.

Which leads to even more stupid shit from your side.

Which leads to me getting kinda angry.

Which leads to me insulting your braindead head.

By weltschmerz - Reply to #569

Incidentally, nonstandard analysis indeed resolves the notational confusion discussed earlier. When looking at the set R^N of all sequences on R for example, we may very well define an equivalence relationship on the subset of convergent sequences by defining two equivalent when they have the same limit. When factoring R^N over that relationship though we end up with something that can't be done useful analysis with, which is pretty much "the" key observation of the whole theory.

So what the nonstandard people do, seeing how convergence, namely "becoming arbitrarily small" on a confinite index set, results in a too coarse equivalence relationship, they refine it and make "being equal" on cofinite index sets the starting point of their model. Which of course is the most intuitive approach you could take when trying to refine the concept to something useful.

Especially, when defining a(n):=1-1/10^n and b(n)=1/10^n, the latter sequence represents an infinitesimal in their model, something not equal to 0 but smaller than any given number on cofinite index sets. And when calling that infinitesimal e for example we do indeed end up with an equation 0.999..+e=1 that properly takes care of all the aspects involved.

So what the nonstandard people do, seeing how convergence, namely "becoming arbitrarily small" on a confinite index set, results in a too coarse equivalence relationship, they refine it and make "being equal" on cofinite index sets the starting point of their model. Which of course is the most intuitive approach you could take when trying to refine the concept to something useful.

Especially, when defining a(n):=1-1/10^n and b(n)=1/10^n, the latter sequence represents an infinitesimal in their model, something not equal to 0 but smaller than any given number on cofinite index sets. And when calling that infinitesimal e for example we do indeed end up with an equation 0.999..+e=1 that properly takes care of all the aspects involved.

By weltschmerz - Reply to #573

Well, look at the tan function for example and consider if you can treat the three series pi/2-1/10^n, pi/2+1/10^n and constant pi/2 as "equal". If you find that you can't and are able to pinpoint the reason then you've found the difference.

A visual aid in case of need: http://de.wikipedia.org/wiki/Datei:Tangent-plot.svg

A visual aid in case of need: http://de.wikipedia.org/wiki/Datei:Tangent-plot.svg

really you shouldn't be capable of being this stupid....

First of all you don't explain how anything that I said is different.

But perhaps more importantly.....

Just 1 post above YOU YOURSELF answer the question.

You are atm trying to confuse people by randomly switching between numerical systems and then just claiming that it's wrong. Because the 2 systems are not perfectly equal.

The only reason why you're doing this is because you realized I was right and now are too proud to admit it.

First of all you don't explain how anything that I said is different.

But perhaps more importantly.....

Just 1 post above YOU YOURSELF answer the question.

You are atm trying to confuse people by randomly switching between numerical systems and then just claiming that it's wrong. Because the 2 systems are not perfectly equal.

The only reason why you're doing this is because you realized I was right and now are too proud to admit it.

Edited by Weird at 15:07 CST, 7 December 2014

By weltschmerz - Reply to #576

Of course I answered the question. Done that a while ago already. But when somebody still asks what the difference was I guess it's ok to provide a hint.

In particular, what nonstandard analysis does is reintroducing that infamous "infinitesimal" that looks like it was nothing but might as well blow up into your face. Anybody who's ever taken the inverse of a small number should know this, shouldn't he.

But then of course, there's those who think that 0.99.. was as good as 1 if you only kept on going "til infinity". Any notable progress you might want to report back in that department anyhow? Hahahahaha ... (til infinity ...)

In particular, what nonstandard analysis does is reintroducing that infamous "infinitesimal" that looks like it was nothing but might as well blow up into your face. Anybody who's ever taken the inverse of a small number should know this, shouldn't he.

But then of course, there's those who think that 0.99.. was as good as 1 if you only kept on going "til infinity". Any notable progress you might want to report back in that department anyhow? Hahahahaha ... (til infinity ...)

By weltschmerz - Reply to #579

Still not? Well, his model suggests that tan(0.5p)= -inf = inf = undefined because his "e" amounts to zero. Obvious enough now?

ahhh omfg thx so much man!!!!!!! I finaly realized the problem we have been adressing for so long!

You can't read.

Really where the f*ck did you get that idea?

I redefined 0 to represent the 'infinitesimal object'.

And after whining of people that they lacked the "real 0" I said that they could allow a notation of 0* if they were so obsessed about a pretty much obsolete symbol.

You can't read.

Really where the f*ck did you get that idea?

I redefined 0 to represent the 'infinitesimal object'.

And after whining of people that they lacked the "real 0" I said that they could allow a notation of 0* if they were so obsessed about a pretty much obsolete symbol.

Edited by Weird at 19:08 CST, 7 December 2014

I think you guys really have some serious miscommunication.because what you described is pretty much exactly what weird came up with. Reintroducing the infinitesimal so that 0.999... +e=1. he then came up with the extremely intuitive notion that inf×e=1 and a lot of confusing notations and mistakes

so to answer the question 0,999... =1? It depends solely on the choice if we want to include infinitesimals or not.

so to answer the question 0,999... =1? It depends solely on the choice if we want to include infinitesimals or not.

you understood me perfectly imho.

Although I dunno what you mean with "confusing notations and mistakes " ;p

Although I dunno what you mean with "confusing notations and mistakes " ;p

Edited by Weird at 19:37 CST, 7 December 2014

Well ye 0 is not "completely useless and obsolete".

But if you were to replace it with an infinitessimal.... it can hold all of it's current important (imo).

Although some would perhaps require a bit of work... Mainly it being the seperator between the positive and negative numbers.

And the definition of 0 - 0 would be fun ofcourse (which is already debated in some thread)

But the possible argumentation in favor / against certain choices is very technical. Not so much philosophically...

But if you were to replace it with an infinitessimal.... it can hold all of it's current important (imo).

Although some would perhaps require a bit of work... Mainly it being the seperator between the positive and negative numbers.

And the definition of 0 - 0 would be fun ofcourse (which is already debated in some thread)

But the possible argumentation in favor / against certain choices is very technical. Not so much philosophically...

By weltschmerz - Reply to #583

No, it doesn't depend on anything. 0.99.. represents the series

0.9

0.99

0.999

and so on. So effectively the series defined by

a(n):=1-1/10^n.

Where the poor clown wrote eg in

http://esreality.com/post/2691593/#pid2687497

that supposedly

0.99999.... = 1

while claiming that you just need to - quoting - "continue on writing 9's infinity many times".

This is like claiming that 1/10^n=0 as n increases. And precisely the point we're talking about. The infinitesimal isn't zero. Which becomes specifically obvious when applying certain functions to it, as we've just done. An observation that doesn't depend on the notion of infinitesimals anyhow, which is merely making more obvious what standard analysis - constantly - tells you to do anyway: distinguish between the sequence and its limit. Because if you don't it might blow up into your face.

So seriously, do I now have yet another one on my hands not being able to make the distinction lying at the very heart of mathematical analysis resp. trying to obfuscate it just to save some dumb face from being exposed as such? If so, what for?

0.9

0.99

0.999

and so on. So effectively the series defined by

a(n):=1-1/10^n.

Where the poor clown wrote eg in

http://esreality.com/post/2691593/#pid2687497

that supposedly

0.99999.... = 1

while claiming that you just need to - quoting - "continue on writing 9's infinity many times".

This is like claiming that 1/10^n=0 as n increases. And precisely the point we're talking about. The infinitesimal isn't zero. Which becomes specifically obvious when applying certain functions to it, as we've just done. An observation that doesn't depend on the notion of infinitesimals anyhow, which is merely making more obvious what standard analysis - constantly - tells you to do anyway: distinguish between the sequence and its limit. Because if you don't it might blow up into your face.

So seriously, do I now have yet another one on my hands not being able to make the distinction lying at the very heart of mathematical analysis resp. trying to obfuscate it just to save some dumb face from being exposed as such? If so, what for?

i don´t get why a number is not a number first and can be obtained by a series. e.g. 1/3 = 0.333... or 0.(3) or 33.(3) % or is 1/3 defined by the series 3*10^(-1)+3*10^(-2)...+3*10^(-n)? or does this not represent 1/3 and you claim there is no way to display the number 1/3?

it's noble of you to ask it as if it is a question...

Pretty good strategy.

You are correct though.

A number is not a number because we can write it down. A number is a number because it represents a value.

For instance nobody can write down pi. Nor can anyone write out 0.33... in any other way than a fraction or by using 'special notation' (like ... or 0.(3)).

Pretty good strategy.

You are correct though.

A number is not a number because we can write it down. A number is a number because it represents a value.

For instance nobody can write down pi. Nor can anyone write out 0.33... in any other way than a fraction or by using 'special notation' (like ... or 0.(3)).

btw it´s funny that the wikipedia article http://en.wikipedia.org/wiki/0.999...

comments on the reluctance of math students to accept that "The equality 0.999... = 1 has long been accepted by mathematicians and is part of general mathematical education"

comments on the reluctance of math students to accept that "The equality 0.999... = 1 has long been accepted by mathematicians and is part of general mathematical education"

I think that everyone except Weltschmerz think that 0.99... = 1.

Even I stated that if you were to have infinitesimals included in math that it would depend a lot on how you describe the math around it if you can still claim 0.99... = 1 or not.

In general though the inclusion of infinitesimals would have to lead to a somewhat different notation.

Conceptually it's not a large change though.

Even I stated that if you were to have infinitesimals included in math that it would depend a lot on how you describe the math around it if you can still claim 0.99... = 1 or not.

In general though the inclusion of infinitesimals would have to lead to a somewhat different notation.

Conceptually it's not a large change though.

By weltschmerz - Reply to #589

Which is rubbish.

To completely formalize it, consider the set R^N of all sequences of real numbers again, together with the canonical injection

R -> R^N

defined by x -> (x, x, x, ...) and element wise operations. Now consider the subset K of convergent sequences, on which you may define a function

lim: K -> R

defined by mapping each sequence to its limit. This function naturally induces an equivalence relation on sequences

a(n) ~ b(n) iff lim(a(n))=lim(b(n)).

So, with respect to this equivalence relation only I might consider those two sequences equal because

lim(0.999...) = lim (1) = 1

But that doesn't make things generally equal of course. Information is lost during the process of merely considering the limit of a sequence and not the sequence itself anymore. And how much information is lost is what we've just seen by means of the tangens or inverse functions.

In particular, the lim function doesn't generally commute with arbitrary other functions, saying that lim*f isn't generally equal f*lim for arbitrary functions f. As we've just seen that the limit of inverses doesn't generally equal the inverse of the limit.

And that's what everybody knows who's ever done the slightest amount of meaningful math in his life. Like working with continuous and non-continuous functions. Differentiating functions. Etcetera etcetera.

So what that article does is merely a notational gimmick by leaving away the "lim" part, which of course anybody, if asked, would tell you is supposed to be implied. And which is a very unfortunate attempt at drawing attention at calculus, because it encourages the kind of total confusion our poor clown here is suffering from.

Which is the reason by the way why nonstandard analysis has developed a model that properly reflects the situation again, specifically also for pedagogical reasons. It basically throws out all that confusing "limit taking" process some simpletons seem to have a hard time wrapping their head around and amends the real numbers with additional, historically very well known, entities like infinitesimals that allow for a representation of the whole picture in terms of pretty much purely algebraic operations:

0.999.. + e = 1

with e an infinitesimal, and you may now entirely forget about the limit taking process there.

So that's the idea, and reportedly it's been quite successful in educational approaches so far. Something the writer of that crappy article, who by the way would readily agree to everything I've said if his education was worth a dime, surely might want to pay some attention to.

To completely formalize it, consider the set R^N of all sequences of real numbers again, together with the canonical injection

R -> R^N

defined by x -> (x, x, x, ...) and element wise operations. Now consider the subset K of convergent sequences, on which you may define a function

lim: K -> R

defined by mapping each sequence to its limit. This function naturally induces an equivalence relation on sequences

a(n) ~ b(n) iff lim(a(n))=lim(b(n)).

So, with respect to this equivalence relation only I might consider those two sequences equal because

lim(0.999...) = lim (1) = 1

But that doesn't make things generally equal of course. Information is lost during the process of merely considering the limit of a sequence and not the sequence itself anymore. And how much information is lost is what we've just seen by means of the tangens or inverse functions.

In particular, the lim function doesn't generally commute with arbitrary other functions, saying that lim*f isn't generally equal f*lim for arbitrary functions f. As we've just seen that the limit of inverses doesn't generally equal the inverse of the limit.

And that's what everybody knows who's ever done the slightest amount of meaningful math in his life. Like working with continuous and non-continuous functions. Differentiating functions. Etcetera etcetera.

So what that article does is merely a notational gimmick by leaving away the "lim" part, which of course anybody, if asked, would tell you is supposed to be implied. And which is a very unfortunate attempt at drawing attention at calculus, because it encourages the kind of total confusion our poor clown here is suffering from.

Which is the reason by the way why nonstandard analysis has developed a model that properly reflects the situation again, specifically also for pedagogical reasons. It basically throws out all that confusing "limit taking" process some simpletons seem to have a hard time wrapping their head around and amends the real numbers with additional, historically very well known, entities like infinitesimals that allow for a representation of the whole picture in terms of pretty much purely algebraic operations:

0.999.. + e = 1

with e an infinitesimal, and you may now entirely forget about the limit taking process there.

So that's the idea, and reportedly it's been quite successful in educational approaches so far. Something the writer of that crappy article, who by the way would readily agree to everything I've said if his education was worth a dime, surely might want to pay some attention to.

Edited by weltschmerz at 12:42 CST, 8 December 2014

So we have a series a (n)=1-1/10^n

This series is infinite and it converges to 1. So why do you think there is information lost if we take the limit of the series? Don't you propose to 'continue til infinity', if you ask to look at the sequence and not it's limit?

This series is infinite and it converges to 1. So why do you think there is information lost if we take the limit of the series? Don't you propose to 'continue til infinity', if you ask to look at the sequence and not it's limit?

By weltschmerz - Reply to #593

Why do I think information is lost by taking the limit? Consider the function f(x):=1/(x-1). And then tell me if lim(f(an))=f(lim(an)). If they aren't the same some information must have been lost somehow, no? Somehow, the limit process seems to treat things as equal which aren't entirely. No?

In other words, lim: K -> R isn't a bijection. In fact, the number of sequences mapping to any given limit has at least the cardinality of R itself. Didn't expect, after so many repetitions of the same basic observations, to again have to point them out.

In other words, lim: K -> R isn't a bijection. In fact, the number of sequences mapping to any given limit has at least the cardinality of R itself. Didn't expect, after so many repetitions of the same basic observations, to again have to point them out.

Edited by weltschmerz at 13:58 CST, 8 December 2014

I'm sure you are a very capable mathematician. I just hoped you could answer my easy non formal questions with easy non formal answers. If this is not possible fair enough. But i don't feel like puttingin the time to learn the formalities if you don't answer my questions. So what about the number 1/3? What is its decimal representation? And what is its representation as a sequence?

Actually that way of writing down a series is kind of confusing.

As you are trying to show the "series" as if it's a "function".

Being that you insert an N and then obtain a number.

Like:

F(1) = 1 - 1 / 10^1 = 0.9

F(2) = 1 - 1 / 10^2 = 0.99

etc.

And that when you insert "inf" intuitively you'd say that you get 0.99...

But this way of writing is not a series but an equation.

A series is written as a sum.

Sum(for x = 0; x < inf) : 9 / 10^x

So you'd write it out as

9 / 10 + 9 / 100 + 9 / 1000 + 9 / 10000 + .....

Which is the same as saying the Sum(for x = 0; x < inf) : 9 / 10^x

This is not really "needed yet" but given that the "function like notation" is intuitively resulting in a number... You'll start making mistakes along the way.

As you are trying to show the "series" as if it's a "function".

Being that you insert an N and then obtain a number.

Like:

F(1) = 1 - 1 / 10^1 = 0.9

F(2) = 1 - 1 / 10^2 = 0.99

etc.

And that when you insert "inf" intuitively you'd say that you get 0.99...

But this way of writing is not a series but an equation.

A series is written as a sum.

Sum(for x = 0; x < inf) : 9 / 10^x

So you'd write it out as

9 / 10 + 9 / 100 + 9 / 1000 + 9 / 10000 + .....

Which is the same as saying the Sum(for x = 0; x < inf) : 9 / 10^x

This is not really "needed yet" but given that the "function like notation" is intuitively resulting in a number... You'll start making mistakes along the way.

Edited by Weird at 13:57 CST, 8 December 2014

By weltschmerz - Reply to #596

Poor fellow, any sequence represents a function. Didn't anybody tell you yet? That's pretty much 2nd day Analysis I.

More specifically, the definition a(n):=1-1/10^n for all natural numbers n defines a function a: N->R. Gee, no wonder you're struggling that hard.

Edit: oh, and any convergent series can be written as sequence and vice versa. Conceptually there's no difference whatsoever. Was that 2nd day or 3rd? Can't really remember anymore.

More specifically, the definition a(n):=1-1/10^n for all natural numbers n defines a function a: N->R. Gee, no wonder you're struggling that hard.

Edit: oh, and any convergent series can be written as sequence and vice versa. Conceptually there's no difference whatsoever. Was that 2nd day or 3rd? Can't really remember anymore.

Edited by weltschmerz at 14:12 CST, 8 December 2014

don't they teach you on day 1 that a series is a SUM of a sequence?

I don't exclude the sequence from having any function, nor do I exclude the sequence from being described using a function. I just state that what you give is not a series.

At the very least it's not the series you want it to be.

Because a(1) = 0.9, a(2) = 0.99

Gives that the sum of just these 2 parts would be 1.89, not 0.99.

I don't exclude the sequence from having any function, nor do I exclude the sequence from being described using a function. I just state that what you give is not a series.

At the very least it's not the series you want it to be.

Because a(1) = 0.9, a(2) = 0.99

Gives that the sum of just these 2 parts would be 1.89, not 0.99.

Edited by Weird at 14:27 CST, 8 December 2014

By weltschmerz - Reply to #599

Quite unsurprisingly you got it mixed up again, poor fellow. A series is defined as a sequence, namely the sequence of its partial sums, and not as "sum of a sequence". Accordingly is the limit of a series defined as the limit of its sequence of partial sums.

Of course, any sequence might also be represented as sequence of partial sums of the differences of its elements. That's why the two concepts are pretty much equivalent.

So, pray tell me, to what level of retardation exactly are you planning to take this?

Edit: oh, and "a" is the sequence of course. In the context of our discussion, I guess not even a chimp would try adding those up.

Of course, any sequence might also be represented as sequence of partial sums of the differences of its elements. That's why the two concepts are pretty much equivalent.

So, pray tell me, to what level of retardation exactly are you planning to take this?

Edit: oh, and "a" is the sequence of course. In the context of our discussion, I guess not even a chimp would try adding those up.

Edited by weltschmerz at 15:12 CST, 8 December 2014

Ahhh so a(x) = 1 - 1 / 10^x

According to yourself is:

**More specifically, the definition a(n):=1-1/10^n for all natural numbers n defines a function a: N->R**

AND

**Edit: oh, and "a" is the sequence of course**

Right.....

So you have a function which is a sequence, which has a single part (1 - 1 / 10^n) which is non recursive.

But it's a sequence none the less....

Ok you lost me....

But well done tricking us into thinking you have a math degree.

According to yourself is:

AND

Right.....

So you have a function which is a sequence, which has a single part (1 - 1 / 10^n) which is non recursive.

But it's a sequence none the less....

Ok you lost me....

But well done tricking us into thinking you have a math degree.

By weltschmerz - Reply to #601

Look poor fellow:

0.9

0.99

0.999

...

was the sequence we're talking about, right?

Now try if you can see how the following equations hold

0.9 = 1-1/10

0.99 = 1-1/10^2

0.999 = 1-1/10^3

or generally

0.99..9 <- n 9s = 1-1/10^n

In other words, a(n):=1-1/10^n for n element of N\{0} is precisely the sequence we're talking about. I'll admit though, some primary school level arithmetic was involved there, so probably a little too much to ask from you to make the connection.

I believe you've kind of answered the question about the level of retardation though, so I guess at least in that department we've made some progress now.

0.9

0.99

0.999

...

was the sequence we're talking about, right?

Now try if you can see how the following equations hold

0.9 = 1-1/10

0.99 = 1-1/10^2

0.999 = 1-1/10^3

or generally

0.99..9 <- n 9s = 1-1/10^n

In other words, a(n):=1-1/10^n for n element of N\{0} is precisely the sequence we're talking about. I'll admit though, some primary school level arithmetic was involved there, so probably a little too much to ask from you to make the connection.

I believe you've kind of answered the question about the level of retardation though, so I guess at least in that department we've made some progress now.

Edited by weltschmerz at 16:08 CST, 8 December 2014

If I recall correctly (omfg ow no it's just a few posts up)

I said the following:

As you are trying to show the "series" as if it's a "function".

Being that you insert an N and then obtain a number.

Like:

F(1) = 1 - 1 / 10^1 = 0.9

F(2) = 1 - 1 / 10^2 = 0.99

etc.

And now you say

0.9 = 1-1/10

0.99 = 1-1/10^2

0.999 = 1-1/10^3

or generally

0.99..9 <- n 9s = 1-1/10^n

Which.... To me! sounds very similar.

And it does not sound like a series.

As to which I commented that:

This is not really "needed yet" but given that the "function like notation" is intuitively resulting in a number... You'll start making mistakes along the way.

I said the following:

As you are trying to show the "series" as if it's a "function".

Being that you insert an N and then obtain a number.

Like:

F(1) = 1 - 1 / 10^1 = 0.9

F(2) = 1 - 1 / 10^2 = 0.99

etc.

And now you say

0.9 = 1-1/10

0.99 = 1-1/10^2

0.999 = 1-1/10^3

or generally

0.99..9 <- n 9s = 1-1/10^n

Which.... To me! sounds very similar.

And it does not sound like a series.

As to which I commented that:

This is not really "needed yet" but given that the "function like notation" is intuitively resulting in a number... You'll start making mistakes along the way.

By weltschmerz - Reply to #603

So, is that what you're having a problem with? That the sequence you brought up - 0.99.. and then adding 9s "til infinity" - results in a sequence of numbers? What did you expect, apples? Gulden? Please share.

I was simply pointing out that what you have created is not a series.

You might call it a series... but it's not.

The correct series would be

Sum(for x = 0; x < inf) : 9 / 10^x

You're also allowed (imo) to use a recursive function like:

F(x) = 9/10^x + F(x+1)

Where you are then forced to call this function with x = 1.

This is me being generous with mathematical notation though...

The difference is that what you're describing is a function, while what I'm describing is a series.

A function outputs a number based on an input, a series doesn't have an input.

You would have a problem like "inf is not a number, so I cannot put it in my function to obtain 0.99...".

Or you would be able to show that your infinitesimal must be a number because you have to insert a number into the function and thus 1 - A(<your number>) = the infinitesimal.

False conclusions like that... Which I am confident that you have many of.

You might call it a series... but it's not.

The correct series would be

Sum(for x = 0; x < inf) : 9 / 10^x

You're also allowed (imo) to use a recursive function like:

F(x) = 9/10^x + F(x+1)

Where you are then forced to call this function with x = 1.

This is me being generous with mathematical notation though...

The difference is that what you're describing is a function, while what I'm describing is a series.

A function outputs a number based on an input, a series doesn't have an input.

You would have a problem like "inf is not a number, so I cannot put it in my function to obtain 0.99...".

Or you would be able to show that your infinitesimal must be a number because you have to insert a number into the function and thus 1 - A(<your number>) = the infinitesimal.

False conclusions like that... Which I am confident that you have many of.

By weltschmerz - Reply to #605

Look poor fellow, if you had properly read that shoddy article you're constantly referring to you'd have understood that your improvised "Sum(for x = 0; x < inf) : 9 / 10^x" needs a definition, because what an "infinite sum" is supposed to mean needs to be defined. And your shoddy article itself says:

"the sum of a series is defined to be the limit of the sequence of its partial sums"

Now make at least a feeble attempt at comprehending, what this would mean for our situation. Like, what would this sequence of partial sums mean to you

0.9

0.9 + 0.09

0.9 + 0.09 + 0.009

...

Do you recognize your much beloved "series" there? Good, because when you add together each of those partial sums - which is generally ok with a finite set of summands even though it might look like a high risk enterprise to you - you end up with this

0.9

0.99

0.999

...

which is exactly the sequence a(n).

Seriously, it's kind of saddening to see you failing so hard at the literally most basic level. And that where I already told you that sequences and series are just two sides of the same coin.

Sad. Very, very sad.

"the sum of a series is defined to be the limit of the sequence of its partial sums"

Now make at least a feeble attempt at comprehending, what this would mean for our situation. Like, what would this sequence of partial sums mean to you

0.9

0.9 + 0.09

0.9 + 0.09 + 0.009

...

Do you recognize your much beloved "series" there? Good, because when you add together each of those partial sums - which is generally ok with a finite set of summands even though it might look like a high risk enterprise to you - you end up with this

0.9

0.99

0.999

...

which is exactly the sequence a(n).

Seriously, it's kind of saddening to see you failing so hard at the literally most basic level. And that where I already told you that sequences and series are just two sides of the same coin.

Sad. Very, very sad.

Edited by weltschmerz at 18:13 CST, 8 December 2014

ok the prev post here (before the edit) was somewhat unnecessarily harsh....

But anyways... if you can't see why I pointed this out and why I'm right....

Well then I'm not the best person to argue further. As I would get pretty damn insulting if I tried and got frustrated :D

But anyways... if you can't see why I pointed this out and why I'm right....

Well then I'm not the best person to argue further. As I would get pretty damn insulting if I tried and got frustrated :D

Edited by Weird at 18:52 CST, 8 December 2014

By weltschmerz - Reply to #607

You know, I really don't give a flying fuck about you. What I care about though are those who might fall for the pretentious and barely understood rubbish you're throwing around. And this particularly in view of a beautiful subject like mathematics, which basically comprises some of the most useful results passed on to us by thousands of years worth of hard working generations. And seeing this gift being abused by you in the most reckless and dumbfounding manner, that's a point for sure where any self respecting person has to feel called upon and intervene.

That you don't understand it doesn't mean that others can't.

This pepidda guy for instance has a lot more understanding about math than you will ever have.

Btw I altered the above post while you were writing yuor reply... And I can somewhat understand your reply as like I said in the edit I was unnecessarily harsh ;)

But on the other side I don't say ANYTHING which would dumb down math.

You on the other hand claim the most rediculous things and can't distinguish between a number and a series. Nor do you have a clear idea of what an infinitesimal is and you're going nuts on really fair remarks made by others.

This pepidda guy for instance has a lot more understanding about math than you will ever have.

Btw I altered the above post while you were writing yuor reply... And I can somewhat understand your reply as like I said in the edit I was unnecessarily harsh ;)

But on the other side I don't say ANYTHING which would dumb down math.

You on the other hand claim the most rediculous things and can't distinguish between a number and a series. Nor do you have a clear idea of what an infinitesimal is and you're going nuts on really fair remarks made by others.

By weltschmerz - Reply to #609

Number and a series?

a(n) isn't a number it's a sequence of numbers, defining a value for each n element of N\{0}. For the twentieth time. And the partial sums of your series are also a sequence. And the sequence of those partial sums is precisely equal to the a(n):=1-1/10^n.

You do realize that it's ok to write 0.9+0.09 as 0.99? I mean, I can see you how would be struggling there, but you really can put an equal sign in between there. 0.9+0.09=0.99 for sure. Trust me just this one time!

Same statement holds for all other elements of the sequence.

a(n) isn't a number it's a sequence of numbers, defining a value for each n element of N\{0}. For the twentieth time. And the partial sums of your series are also a sequence. And the sequence of those partial sums is precisely equal to the a(n):=1-1/10^n.

You do realize that it's ok to write 0.9+0.09 as 0.99? I mean, I can see you how would be struggling there, but you really can put an equal sign in between there. 0.9+0.09=0.99 for sure. Trust me just this one time!

Same statement holds for all other elements of the sequence.

Dunno what you're babbling about.

It seems like you either confuse a number with a digit... Or a number with a series... Or a function with a series... or something....

I dunno.

0.9 + 0.09 = 0.99 yes.

Just like 1 - 0.01 = 0.99

But:

0.9 + 0.09 + 0.009 + .... is a series of infinit length

0.9 + 0.09 + 0.009 could be read as a series of length 3. (it's not regularly done so but I do this as an example)

While

1 - 0.001 is not a series of length 3.

It's equal to the number you get when you run through the series of 0.9 + 0.09 + 0.009 but it is not a series.

It seems like you either confuse a number with a digit... Or a number with a series... Or a function with a series... or something....

I dunno.

0.9 + 0.09 = 0.99 yes.

Just like 1 - 0.01 = 0.99

But:

0.9 + 0.09 + 0.009 + .... is a series of infinit length

0.9 + 0.09 + 0.009 could be read as a series of length 3. (it's not regularly done so but I do this as an example)

While

1 - 0.001 is not a series of length 3.

It's equal to the number you get when you run through the series of 0.9 + 0.09 + 0.009 but it is not a series.

By weltschmerz - Reply to #611

You still didn't understand your shoddy article? So here it is again:

0.9 + 0.09 + 0.009 + .... needs to be defined. And the very definition is the sequence

0.9

0.9+0.09

0.9+0.09+0.009

...

Each line there makes for a so called "partial sum". And the sequence of lines is the sequence of partial sums. Which is exactly my sequence a(n), which should be easy enough to see if you're capable of basic addition.

I mean, I know I probably have to repeat it to you a gazillion times now, so I'll take the liberty and just refer you here to

http://en.wikipedia.org/wiki/Series_%28mathematics%29#Definition

Feel free to report back when you've understood a single thing. But please check with somebody else first, that it is really the case.

0.9 + 0.09 + 0.009 + .... needs to be defined. And the very definition is the sequence

0.9

0.9+0.09

0.9+0.09+0.009

...

Each line there makes for a so called "partial sum". And the sequence of lines is the sequence of partial sums. Which is exactly my sequence a(n), which should be easy enough to see if you're capable of basic addition.

I mean, I know I probably have to repeat it to you a gazillion times now, so I'll take the liberty and just refer you here to

http://en.wikipedia.org/wiki/Series_%28mathematics%29#Definition

Feel free to report back when you've understood a single thing. But please check with somebody else first, that it is really the case.

a sequence is a set of numbers....

Taking the sum of certain elements of a sequence of numbers is called the "partial sum".

Taking the "partial sum" of all of the elements is called "a series".

In none of the above situations is what you described the wanted series.

You are allowed to call it a sequence though if you'd say that a(n) describes the set of "A" which has "n" members.

But the members would be {0.9, 0.99, 0.999, 0.9999....}

The series of this set would be close to 1.9 (not the exact limit btw...)

Dunno where you want to blame me for your failing.

Taking the sum of certain elements of a sequence of numbers is called the "partial sum".

Taking the "partial sum" of all of the elements is called "a series".

In none of the above situations is what you described the wanted series.

You are allowed to call it a sequence though if you'd say that a(n) describes the set of "A" which has "n" members.

But the members would be {0.9, 0.99, 0.999, 0.9999....}

The series of this set would be close to 1.9 (not the exact limit btw...)

Dunno where you want to blame me for your failing.

Sorry for comming so late to the nerd party.

What was the question you guys were discussing? With the limit thing? If '1 = 0.99...' ? To answer this question one should first agree about the context in which both sides of the equation are to be taken. They certainly are not equal as unicode strings, for example =)

If we consider '2=1+1', an equation that most people would certainly agree holds, then both sides also dont agree as strings. So to come to the conclusion, that "2=1+1" holds "mathematically" one has to interpret both sides first.

You can think of this as a type declaration in computer science. If you want to compare two objects and assign a boolean value to the outcome of this test, then they have to be instances of the same class and this class has to have an "equality operator". You can't compare the integer 5 with the string "QUAD NOW!", for example.

Stretching it a bit, one could also interpret both sides of "2=1+1" as finite formal sums of integers. A bit like a (finite) one-dimensional array of integers. Then the left hand side is the array [2] and the right hand side is [1,1]. These don't even have the same dimensions, so can't be equal as arrays. If we try really hard to interpret them as equal, we could try to see the left hand side as the array [2,0] but still, this is different from [1,1]. If we use "," or "+" in our notation of an array really makes no difference, as long as we treat the symbol as a formal seperator, not as an addition operator of the entries.

What, if we actually treat "+" as an operator on integers, like many people would automatically do, when presented with the equation "2=1+1"? Of course, 1+1 yields an integer. So we can compare both sides in the realms of integers. Both sides agree as integers, but not as strings!

Clarifying what we mean by the expression "0.99...." and choosing the correct realm where to interpret the "="-test with "1" is equally easy. Let's be clear about the definitions, then the answer will present itself to us =)

a) If by "0.99...." we mean a string, then the string "1" is not equal to this string.

b) If by "0.99..." we mean the sequence of formal (!) finite sums

S_n="0*10^0+9*10^(-1)+...+9*10^(-n)" for n positive integer and by "1" we mean the sequence of formal finite sums

T_n="1*10^0+0*10^(-1)+...+0*10^(-n)" then these two sequences don't agree. This is trivial, since the equality of sequences is checked by looking at each index (like string comparison) and S_n is different from T_n, not only for some n, but even for all n!

c) What if we interpret the "+" in the formal finite sums of b) as addition operator? This led us to the tremendous insight, that "2=1+1". Maybe it will do the trick again?

So "0.99..." stands for a sequence (indexed by natural numbers n) of rational numbers 0.9, 0.99, 0.999 etc. "1" stands for the constant sequence 1, 1, 1, etc. Of course, these are different sequences, so "1=0.99..." is false in this sense.

So it seems the two expressions are not equal, after all? Until now, all comparisons looked pretty formal, no convergence/limit/neighbourhood considerations at all! Well, it gets a little more complicated but also more interesting, if you introduce what is called a "metric" on the rationals and realize there are some special sequences of rational numbers:

As soon as you realize 1*1=1 and 2*2=4 and 1<2<4 you might ask yourself, is there some number x, such that x*x=2. If it exists, it should possibly be somewhere between 1 and 2. It turns out (and Euklid showed this) that there is no rational number x with this property. On the other hand there are sequences a(n) of rational numbers that have the property that a(n)*a(n) comes arbitrarily close to 2 for growing n.

We very much would like to use these sequence a(n) just as a rational number and treat like the square root of 2. Turns out, this idea brings you very close to the definition of the real numbers!

The only problem is: If we have two series of rational numbers, that have the property that their squares come arbitrarily close to 2, which one should we take to be "the" square root of 2?

And this problem will certainly occur, since if we take some nice sequence a(n) with a(n)*a(n) coming closer and closer to 2, then just change some entries at the beginning of a and you will end up with another nice sequence, different form a, that you would also like to call the square root of 2.

Now comes THE definition ((c) by A.-L. Cauchy~1820) that will resolve all problems :

A real number is defined to be an equivalence class of sequences of rational numbers, such that late members of the sequences lie arbitrarily close ("Cauchy-sequence"). Here, two such sequences are called equivalent, if they differ only by a sequence that comes arbitrarily close to the constant 0-sequence.

THIS IS IT. I never said, Calculus was easy. =) Once you understand this definition and its implications, you can truly and honestly admire the beauty of it, discuss limits with people on the internet and go-on with the rest of your 1-st semester curriculum =) Honestly, I think this is the most important and hardest to grasp definition in every math students education.

Coming back to "1=0.99...":

Interpreted as real numbers, the left hand side represents the equivalence class of the constanst sequence of rational numbers a(n)=1, 1, 1,...

The right hand side represents the equivalence class of the sequence b(n)= 0, 0.9, 0.99, ... of rational numbers.

Are these Cauchy-sequences? Yes! Constant sequences are always Cauchy (trivial exercise, that you should do). And b(n)-b(m)=0.0...009...9 with m 0's in the middle and (n-m) 9's at the end. So b(n)-b(m)<0.0...01=10^(-m) for all n>m and hence this is Cauchy.

Hence both sequences of rationals represent real numbers! But do they agree??? Yes! Because, a(n)-b(n)=10^(-n) and this comes arbitrarily close to the constant 0 sequence. Hence by definition both sequences lie in the same equivalence class and are equal as real numbers. That was easy!

tldr: 1=0.99... when interpreted as real numbers: The Cauchy-sequences they represent, differ only by a sequence tending to zero.

What was the question you guys were discussing? With the limit thing? If '1 = 0.99...' ? To answer this question one should first agree about the context in which both sides of the equation are to be taken. They certainly are not equal as unicode strings, for example =)

If we consider '2=1+1', an equation that most people would certainly agree holds, then both sides also dont agree as strings. So to come to the conclusion, that "2=1+1" holds "mathematically" one has to interpret both sides first.

You can think of this as a type declaration in computer science. If you want to compare two objects and assign a boolean value to the outcome of this test, then they have to be instances of the same class and this class has to have an "equality operator". You can't compare the integer 5 with the string "QUAD NOW!", for example.

Stretching it a bit, one could also interpret both sides of "2=1+1" as finite formal sums of integers. A bit like a (finite) one-dimensional array of integers. Then the left hand side is the array [2] and the right hand side is [1,1]. These don't even have the same dimensions, so can't be equal as arrays. If we try really hard to interpret them as equal, we could try to see the left hand side as the array [2,0] but still, this is different from [1,1]. If we use "," or "+" in our notation of an array really makes no difference, as long as we treat the symbol as a formal seperator, not as an addition operator of the entries.

What, if we actually treat "+" as an operator on integers, like many people would automatically do, when presented with the equation "2=1+1"? Of course, 1+1 yields an integer. So we can compare both sides in the realms of integers. Both sides agree as integers, but not as strings!

Clarifying what we mean by the expression "0.99...." and choosing the correct realm where to interpret the "="-test with "1" is equally easy. Let's be clear about the definitions, then the answer will present itself to us =)

a) If by "0.99...." we mean a string, then the string "1" is not equal to this string.

b) If by "0.99..." we mean the sequence of formal (!) finite sums

S_n="0*10^0+9*10^(-1)+...+9*10^(-n)" for n positive integer and by "1" we mean the sequence of formal finite sums

T_n="1*10^0+0*10^(-1)+...+0*10^(-n)" then these two sequences don't agree. This is trivial, since the equality of sequences is checked by looking at each index (like string comparison) and S_n is different from T_n, not only for some n, but even for all n!

c) What if we interpret the "+" in the formal finite sums of b) as addition operator? This led us to the tremendous insight, that "2=1+1". Maybe it will do the trick again?

So "0.99..." stands for a sequence (indexed by natural numbers n) of rational numbers 0.9, 0.99, 0.999 etc. "1" stands for the constant sequence 1, 1, 1, etc. Of course, these are different sequences, so "1=0.99..." is false in this sense.

So it seems the two expressions are not equal, after all? Until now, all comparisons looked pretty formal, no convergence/limit/neighbourhood considerations at all! Well, it gets a little more complicated but also more interesting, if you introduce what is called a "metric" on the rationals and realize there are some special sequences of rational numbers:

As soon as you realize 1*1=1 and 2*2=4 and 1<2<4 you might ask yourself, is there some number x, such that x*x=2. If it exists, it should possibly be somewhere between 1 and 2. It turns out (and Euklid showed this) that there is no rational number x with this property. On the other hand there are sequences a(n) of rational numbers that have the property that a(n)*a(n) comes arbitrarily close to 2 for growing n.

We very much would like to use these sequence a(n) just as a rational number and treat like the square root of 2. Turns out, this idea brings you very close to the definition of the real numbers!

The only problem is: If we have two series of rational numbers, that have the property that their squares come arbitrarily close to 2, which one should we take to be "the" square root of 2?

And this problem will certainly occur, since if we take some nice sequence a(n) with a(n)*a(n) coming closer and closer to 2, then just change some entries at the beginning of a and you will end up with another nice sequence, different form a, that you would also like to call the square root of 2.

Now comes THE definition ((c) by A.-L. Cauchy~1820) that will resolve all problems :

A real number is defined to be an equivalence class of sequences of rational numbers, such that late members of the sequences lie arbitrarily close ("Cauchy-sequence"). Here, two such sequences are called equivalent, if they differ only by a sequence that comes arbitrarily close to the constant 0-sequence.

THIS IS IT. I never said, Calculus was easy. =) Once you understand this definition and its implications, you can truly and honestly admire the beauty of it, discuss limits with people on the internet and go-on with the rest of your 1-st semester curriculum =) Honestly, I think this is the most important and hardest to grasp definition in every math students education.

Coming back to "1=0.99...":

Interpreted as real numbers, the left hand side represents the equivalence class of the constanst sequence of rational numbers a(n)=1, 1, 1,...

The right hand side represents the equivalence class of the sequence b(n)= 0, 0.9, 0.99, ... of rational numbers.

Are these Cauchy-sequences? Yes! Constant sequences are always Cauchy (trivial exercise, that you should do). And b(n)-b(m)=0.0...009...9 with m 0's in the middle and (n-m) 9's at the end. So b(n)-b(m)<0.0...01=10^(-m) for all n>m and hence this is Cauchy.

Hence both sequences of rationals represent real numbers! But do they agree??? Yes! Because, a(n)-b(n)=10^(-n) and this comes arbitrarily close to the constant 0 sequence. Hence by definition both sequences lie in the same equivalence class and are equal as real numbers. That was easy!

tldr: 1=0.99... when interpreted as real numbers: The Cauchy-sequences they represent, differ only by a sequence tending to zero.

Edited by m0n0_ at 13:44 CST, 10 December 2014

I would agree with you, Weltschmerz would not.

That's around 90pc of the latest posts...

However the whole thing started going berzerk when, a year ago, I made a note of a certain (imo) intuitive notion of infinitesimals to explain how you could change parts of math in order to have a difference between 0.99.. and 1.

Namely to "reform the notation 0 to an infinitesimal" where this infinitesimal would be infinitely close to 0.

To achieve this we rewrite (this new) 0 as 1 / inf.

And then one could use that notation to claim that 1 - 0 = 0.99...

and that 0.99.. + 0 = 1.

Now this notation has a lot of (extremely logical) if's and buts accompanied with it... Which I all answered while others went full retard.

When they then started to repeat their questions I got a bit pissed ;)

The misunderstanding existing because if you define 0 to be 1 / inf it's not within the reals anymore, yet 0 - 0 would be within the reals (namely being what is the current 0 in the real numbers).

And the "same notation" of 0 while it resembles something slightly different made people go mental.

Even though you can treat an infinitesimal 0 almost the same as you do with the "real 0".

That's around 90pc of the latest posts...

However the whole thing started going berzerk when, a year ago, I made a note of a certain (imo) intuitive notion of infinitesimals to explain how you could change parts of math in order to have a difference between 0.99.. and 1.

Namely to "reform the notation 0 to an infinitesimal" where this infinitesimal would be infinitely close to 0.

To achieve this we rewrite (this new) 0 as 1 / inf.

And then one could use that notation to claim that 1 - 0 = 0.99...

and that 0.99.. + 0 = 1.

Now this notation has a lot of (extremely logical) if's and buts accompanied with it... Which I all answered while others went full retard.

When they then started to repeat their questions I got a bit pissed ;)

The misunderstanding existing because if you define 0 to be 1 / inf it's not within the reals anymore, yet 0 - 0 would be within the reals (namely being what is the current 0 in the real numbers).

And the "same notation" of 0 while it resembles something slightly different made people go mental.

Even though you can treat an infinitesimal 0 almost the same as you do with the "real 0".

By madbringer

Were the big changes that it's going to suck a massive amount of black dicks and it'll die a slow and painful death?