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Interesting fact: 0.99999... = 1

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Poreuomai Minmatar Mirkur Draug'Tyr Ushra'Khan	Posted - 2009.05.15 12:39:00 - [61] Edited by: Poreuomai on 15/05/2009 12:39:21 1=0.99999... is really easy to prove: 3(1/3) = 3 0.333333... = 0.999999... *Let My People Go*
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.15 12:41:00 - [62] Originally by: Whitehound Originally by: ReaperOfSly You can't treat 1/9 as the actual 1/9 (that is, a ninth) because the first line of your proof was "Let 1/9 = 0.1111111...". That's you defining what 1/9 means, you then have to prove that it is actually equal to one ninth. Your conclusion is correct, but your proof is invalid. I am not defining what "1/9" is, I am defining what "0.1" is equal to. It is a know fact that 1/9 equals to 0.1 or 0.111..., and it is well accepted. You may have an interest in mathematics, but, please, do what I did. Study it. I did. Apparently in more depth than you did. ____________________
Lord Zoran House of Tempers	Posted - 2009.05.15 14:17:00 - [63] i'm thinking more along the lines of why did you bother making a thread about something as pointless as this
Feilamya Minmatar	Posted - 2009.05.15 18:28:00 - [64] Edited by: Feilamya on 15/05/2009 18:28:46 All those "..." proofs may seem more intuitive than the "lim"/"sum" stuff. However, in maths, intuition can go badly wrong. Ask yourself the following questions. Try to answer them by intuition. I assure you, if you don't know the right answers, you will get it wrong: Let N be the natural numbers, Z be the integer numbers, Q be the rational numbers and R be the real numbers. Everyone should have heard of these in school... N = {0, 1, 2, 3, ... } Z = {..., -3, -2, -3, 0, 1, 2, 3, ... } Q = {a/b \| a, b in Z} R = uhm ... you know, Q plus the weird stuff like PI, e and square roots of seemingly harmless numbers like 2 ... So, how many numbers are there? 1. Are N and Z the same size? If not, what is the size of Z compared to N? 2. Are Z and Q the same size? If not, what is the size of Q compared to Z? 2. Are Q and R the same size? If not, what is the size of R compared to Q? There are at least two intuitive answers to all question which are both wrong for at least one of them.
Devine13 Nomad LLP	Posted - 2009.05.15 22:17:00 - [65] Originally by: Poreuomai Edited by: Poreuomai on 15/05/2009 12:39:21 1=0.99999... is really easy to prove: 3(1/3) = 3 0.333333... = 0.999999... THIS, I was just about to post the exact same thing but I decided I'd read through the thread first to see if somebody already said that lol
Whitehound	Posted - 2009.05.16 00:54:00 - [66] Originally by: ReaperOfSly I did. Apparently in more depth than you did. Certainly not. Stop making a fool of yourself about something as little as this. -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
Whitehound	Posted - 2009.05.16 01:12:00 - [67] Originally by: Feilamya So, how many numbers are there? A lot! It is one of the earliest things you learn in mathematics. The numbers in N can be counted from 1 to Infinity. The numbers in Z can be counted, too, by counting 0, 1, -1, 2, -2, ... The numbers in Q can be counted with the help of Cantor's diagonal method. And the numbers in R are uncountable, because there are as "many" numbers between 0 and 1 as there are between 1 and 2, and at the same time between 1 and infinity. See Abel's proof. Seriously, no one who did not study mathematics will care about this. -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
Bestofworst Gallente Double Eagle Enterprises	Posted - 2009.05.16 01:35:00 - [68] Originally by: Taedrin Edited by: Taedrin on 08/05/2009 04:21:55 Edited by: Taedrin on 08/05/2009 04:21:35 That proof actually makes no sense to me, as you are performing arithmetic with infinity (a number which extends into infinity, to be specific). What you REALLY want to say is this: x lim x->inf ∑ 9/(10^x) = 1 1 Here the concept of infinity is restricted to end behavior analysis, and you don't have to do any arithmetic with it. I understood that! clap ---- <Insert Wit>
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.16 08:09:00 - [69] Originally by: Whitehound Originally by: ReaperOfSly I did. Apparently in more depth than you did. Certainly not. Stop making a fool of yourself about something as little as this. Well you're an oddity. You know about Cantor's diagonalisation proof, but fail to notice that your earlier proof has a gaping hole in it even when it's pointed out. I'm guessing, first year university student then? Or someone studying it in your spare time? Or maybe you're a top university lecturer and are therefore allowed to say "it's obvious"? ____________________
Whitehound	Posted - 2009.05.16 09:39:00 - [70] Edited by: Whitehound on 16/05/2009 09:47:56 Originally by: ReaperOfSly Well you're an oddity. You know about Cantor's diagonalisation proof, but fail to notice that your earlier proof has a gaping hole in it even when it's pointed out. I'm guessing, first year university student then? Or someone studying it in your spare time? Or maybe you're a top university lecturer and are therefore allowed to say "it's obvious"? Get lost, stupid. You want to call 1/9 a quantity? And, yes, it is obvious. You are taking the proof out of its context. -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
Kazuo Ishiguro House of Marbles Zzz	Posted - 2009.05.16 11:30:00 - [71] If one allows your premise that 1/9 = 0.111... , then your conclusion certainly follows. Suppose I asked you to prove that 1/9 = 0.111... ? I'm sure you can do that, it's just that you haven't actually done it yet. The whole point of this discussion is that proving that infinite decimals are convergent is not as trivial as it might appear. Also, since people are talking about R, N, Z and Q, here's another one for you. Is there another infinite set larger than N but smaller than R? --- 20:1 mineral compression ISRC Racing, Season 7 - schedule
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.16 11:34:00 - [72] Originally by: Whitehound Get lost, stupid. You want to call 1/9 a quantity? Nope. You did when you said "Let 1/9 = 0.11111...". (And stop being so aggressive, it makes you look childish) ____________________
Shadow Devourer	Posted - 2009.05.16 14:44:00 - [73] Originally by: Kazuo Ishiguro Also, since people are talking about R, N, Z and Q, here's another one for you. Is there another infinite set larger than N but smaller than R? Hi there mr Cantor.
Whitehound	Posted - 2009.05.16 19:49:00 - [74] Originally by: ReaperOfSly Nope. You did when you said "Let 1/9 = 0.11111...". No, I did not and I am not going to give you a lecture in mathematics. Get lost now, stupid. -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.16 21:18:00 - [75] Originally by: Whitehound Originally by: ReaperOfSly Nope. You did when you said "Let 1/9 = 0.11111...". No, I did not and I am not going to give you a lecture in mathematics. Get lost now, stupid. Ah, the classic response of someone who cannot defend his argument and is still trying to save face. I've gotten bored arguing with you, so I shall grant your wish and leave the thread. ____________________
Whitehound	Posted - 2009.05.16 22:27:00 - [76] Originally by: ReaperOfSly I've gotten bored arguing with you, so I shall grant your wish and leave the thread. Thank you!! -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
Incantare	Posted - 2009.05.17 01:53:00 - [77] Edited by: Incantare on 17/05/2009 01:54:40 Originally by: Kazuo Ishiguro Technically, people using the OP's proof are making the assumption that the sum of the terms in the decimal expansion is convergent. If it isn't, the proof fails at the 10n - n stage, as the result would still be infinite. There's no need to worry about problems of convergence - although it can be done by bounding with increasing and decreasing expressions that both have the same limit it's completly unecessary. Because the limit of the series is easily obtained. Originally by: ReaperOfSly Originally by: Whitehound Get lost, stupid. You want to call 1/9 a quantity? Nope. You did when you said "Let 1/9 = 0.11111...". This is the proof you are looking for.
Whitehound	Posted - 2009.05.17 19:00:00 - [78] Originally by: Incantare This is the proof you are looking for. Edit: there's an extra 0 in line two, it should read 1/900 not 1/9000. Do not support him, please. You are only going to make his life worse. On the side, mathematics only originates from philosophy, but it is not the same as philosophy. It is a science of nature and shall be treated as such. Its purpose is the study of nature, and not to win arguments or to find the meaning of life. Does anyone know why there is no Nobel price for mathematics? -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.17 19:08:00 - [79] Originally by: Whitehound Originally by: Incantare This is the proof you are looking for. Edit: there's an extra 0 in line two, it should read 1/900 not 1/9000. Do not support him, please. You are only going to make his life worse. On the side, mathematics only originates from philosophy, but it is not the same as philosophy. It is a science of nature and shall be treated as such. Its purpose is the study of nature, and not to win arguments or to find the meaning of life. Does anyone know why there is no Nobel price for mathematics? It's called a Fields Medal. ____________________
Whitehound	Posted - 2009.05.17 19:26:00 - [80] Edited by: Whitehound on 17/05/2009 19:28:22 Originally by: ReaperOfSly Originally by: Whitehound Does anyone know why there is no Nobel price for mathematics? It's called a Fields Medal. No. The Fields Medal is a price exclusively for mathematicians, but is not the same as the Nobel Prize. The Nobel Prize is awarded for many sciences. Some see the Fields Medal as the "Nobel Price of mathematics", but they are being - you may have guessed it - stupid. Fact is, and always will be, that mathematicians cannot win the Nobel Prize. There exists a rumour why Nobel excluded mathematics. Do you know it? For the lazy, the Wikipedia entry to the Nobel Prize mentions it. -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
Whitehound	Posted - 2009.05.17 22:23:00 - [81] Originally by: Kazuo Ishiguro The whole point of this discussion is that proving that infinite decimals are convergent is not as trivial as it might appear. No, and I will give you an explanation. There is no such thing as infinite decimals. If a person would sit done to create just a single infinite decimal then that person would still be working on it and therefore such a thing cannot exist. You may think of them as being infinite decimals, made of an infinite sequence of numbers, but it is really just an illusion in your head. One cannot possibly imagine such a number, because a brain is made only of a finite amount of neurons. We then use notations like 1/9, 0.1, 0.111..., (or pi and e) to have a finite representation for these numbers. These are however numbers just like any other number, there is nothing special about them, and there is nothing convergent (or non-convergent) about them. Only for when we analyse sequences and series do we use the term convergent. You then can use a convergent series to represent such a number, but it does not make the number convergent. The reason why the proof of "0.9 = 1" exists is only to show that they both represent the same, identical number. There is no other point to it. Why is no one making a proof 1/9 being equal to 0.1? Because 1/9 is not a number but an expression. The same goes for the number pi. No one makes a proof of 3.14159... being equal to pi. So, please, stop indulging yourself in proofs mankind does not need. -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.18 11:55:00 - [82] Originally by: Whitehound So, please, stop indulging yourself in proofs mankind does not need. Now I KNOW you've never studied maths. Maths is all about the proofs. The reason for that is that intuition can and will lead you astray, especially when dealing with anything to do with infinity. You need a proof to make sure that isn't happening. For example, think of a continuous, zero-thickness curve. Is it possible to completely fill a two-dimensional region by folding and bending this curve? Intuition would say no, formal mathematical reasoning says yes. ____________________
Whitehound	Posted - 2009.05.18 12:53:00 - [83] Originally by: Stupid Maths is all about the proofs. No, and I will not tell you why. Find it out for yourself. Originally by: Stupid For example, think of a continuous, zero-thickness curve. Is it possible to completely fill a two-dimensional region by folding and bending this curve? Intuition would say no, formal mathematical reasoning says yes. I took part in a workshop in 1995 at the IGD/FhG in Germany, held by H.J. Peitgen and Prof. J.L. Encarnatpo. I have to admit that I did not understand all of it as it was all pretty new. But, yes, I am familiar with the curve and some of fractal geometry. Allow me to ask you something in return. Do you know when it fails to fill a space? -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.18 14:12:00 - [84] Originally by: Whitehound Edited by: Whitehound on 18/05/2009 13:20:00 Originally by: Stupid Maths is all about the proofs. No, and I will not tell you why. Find it out for yourself. I gave you a perfectly valid reason for my assertion, you can at least return the courtesy. Quote: Originally by: Stupid For example, think of a continuous, zero-thickness curve. Is it possible to completely fill a two-dimensional region by folding and bending this curve? Intuition would say no, formal mathematical reasoning says yes. I took part in a workshop in 1995 at the IGD/FhG in Germany, held by H.J. Peitgen and Prof. J.L. Encarnatpo. I have to admit that I did not understand all of it as it was all pretty new. But, yes, I am familiar with it and some of fractal geometry. Allow me to ask you something in return. Do you know when it fails to fill a space? I admit I do not. At a guess, I would say it fails if it is differentiable, or rather is is non-differentiable only at a countable number of points. It might also fail in a number of weird topologies. What was this workshop about? I'm not familiar with those names. Quote: And do not call it a curve, because it does not curve like a continuous function. It is a fractal function. The Hilbert Curve (and every other space filling curve I am aware of) IS continuous. I think you're confusing "continuous" with "differentiable". And "curve" is a perfectly good word to describe it. ____________________
Whitehound	Posted - 2009.05.18 18:21:00 - [85] Edited by: Whitehound on 18/05/2009 18:24:11 Originally by: ReaperOfSly The Hilbert Curve (and every other space filling curve I am aware of) IS continuous. I think you're confusing "continuous" with "differentiable". And "curve" is a perfectly good word to describe it. No, it is not what I have said and you could have asked. Instead do you choose to take it wrong every single time. Therefore will I not exchange any courtesies with you ..... A curve like f(x)=x^2 always evaluates into a single number for any single x. It then does not matter if f(x) really is continuous or differentiable. What does matter is that it can return at best only another interval f(x) for any interval of x. The best you can get is a injective/bijective function and where every x evaluates into a unique f(x). The worst is a surjective function where every x results in the same number, i.e. f(x)=0. The Hilbert Curve H(n) always results in an entire curve for any single n, and not just a single number! It is therefore not like any other 1-dimensional function, but a 2-dimensional function of H(n,x), which is why I choose to call it a fractal function and say that it does not curve in the usual sense. H(n,x) can then only fill a finite 2-dimensional space, but not an infinite one, because n, while it is going towards infinity, is only an element of N, which is a countable finite set. It therefore is not like any other 2-dimensional function, but a special case, and another good reason to call it a fractal function. -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
Imertu Solientai Gallente	Posted - 2009.05.18 23:12:00 - [86] Originally by: Whitehound Edited by: Whitehound on 18/05/2009 13:20:00 Originally by: Stupid Maths is all about the proofs. No, and I will not tell you why. Find it out for yourself. I don't care how many PHD's and Degrees you have. This quote shows that you are STUPID! (bolded for extra emphasis) CLEAR SKIES 2 IS OUT! PLEASE SEED!
Whitehound	Posted - 2009.05.19 07:55:00 - [87] Edited by: Whitehound on 19/05/2009 08:04:06 Originally by: Imertu Solientai I don't care how many PHD's and Degrees you have. This quote shows that you are STUPID! (bolded for extra emphasis) Yeah, right. And the use of bold and underline makes you what? You are stupid #2. And to make this perfectly clear. If there is something you do not understand, then do not expect others to explain it to you every single time. You are old enough to find out for yourself. I am not asking you to be grateful for when you get an explanation, because I know that you suckers cannot be grateful. -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.19 12:42:00 - [88] Originally by: Whitehound Edited by: Whitehound on 19/05/2009 08:45:02 Originally by: Imertu Solientai I don't care how many PHD's and Degrees you have. This quote shows that you are STUPID! (bolded for extra emphasis) Yeah, right. And the use of bold and underline makes you what? You are stupid #2. And to make this perfectly clear. If there is something you do not understand, then do not expect others to explain it to you every single time. You are old enough to find out for yourself. If you cannot find it then try to ask! I am not asking you to be grateful for when you get an explanation, because I know that you kids cannot be grateful, but asking is very simple to do. But you ARE expected to back up wild assertions with some reasoning. There's a difference between doing someone's work for them, and putting forward an argument to defend your assertion. It's not even a subtle difference. ____________________
Whitehound	Posted - 2009.05.19 13:35:00 - [89] Originally by: ReaperOfSly But you ARE expected to back up wild assertions with some reasoning. It is just as much expected for you to ask before you call it a "wild" assertion. Say, why do you call it wild? -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.19 13:41:00 - [90] Edited by: ReaperOfSly on 19/05/2009 13:42:09 Originally by: Whitehound Originally by: ReaperOfSly But you ARE expected to back up wild assertions with some reasoning. It is just as much expected for you to ask before you call it a "wild" assertion. Say, why do you call it wild? If you recall, I made a statement and provided an explanation to back it up. You simply contradicted me without giving a reason. In fact, you went out of your way to say you weren't going to give a reason. That's called a wild assertion. ____________________

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