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Interesting fact: 0.99999... = 1

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Hobgoblin ll	Posted - 2009.05.08 03:03:00 - [1] Proof: Let n = 0.999... Then 10n = 9.99... 10n - n = 9.999... - 0.999... 9n = 9.000... 9n = 9 n = 9/9 = 1
Atomos Darksun Damage Incorporated.	Posted - 2009.05.08 03:07:00 - [2] Not really, no. Originally by: Amoxin My vent is talking to me in a devil voice... CONVERT TO LINKIFICATION! http://myeve.eve-online.com/ingameb
Intense Thinker Minmatar	Posted - 2009.05.08 03:19:00 - [3] I want to say you're not doing it right, but I suck at math so I can't Pomp FTW!!!
Atomos Darksun Damage Incorporated.	Posted - 2009.05.08 03:41:00 - [4] Originally by: Intense Thinker I want to say you're not doing it right, but I suck at math so I can't Great name. Originally by: Amoxin My vent is talking to me in a devil voice... CONVERT TO LINKIFICATION! http://myeve.eve-online.com/ingameb
Lance Fighter Amarr	Posted - 2009.05.08 03:57:00 - [5] actually hes doing it right. Originally by: Akita T Seriously ? ...wow... I'm such a forum ho' !
Dong Ninja	Posted - 2009.05.08 04:01:00 - [6] It's a given that .999...=1 because in your first part of the proof you said that n=.999... You might as well have said n = 1, because any number continuing on into infinity will grow. I'll put it another way: if n=.999... then n-.000..1 will never be reached, thus there is nothing being subtracted, so n=1. Originally by: Xen Gin Indeed, upgrading an MS OS is like taking a **** into a cake mixture, then complaining that it doesn't taste good when it's all done.
Taedrin Gallente Golden Mechanization Protectorate	Posted - 2009.05.08 04:21:00 - [7] 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.
goodby4u Valor Inc. Psychotic Tendencies.	Posted - 2009.05.08 04:24:00 - [8] I dont like these threads, they make me feel stupid.
Lance Fighter Amarr	Posted - 2009.05.08 04:29:00 - [9] 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. the proof makes perfect sense, as long as you assume that 0.99... is a number, that when subtracted from itself, gives you 0.. which.. um.. it does. Originally by: Akita T Seriously ? ...wow... I'm such a forum ho' !
Hobgoblin ll	Posted - 2009.05.08 05:17:00 - [10] Originally by: Lance Fighter 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. the proof makes perfect sense, as long as you assume that 0.99... is a number, that when subtracted from itself, gives you 0.. which.. um.. it does. This. Can be easy proven with fractions aswell: 0.111... = 1/9 9x 0.111... = 9 x (1/9) = 9/9 = 1 therefore 0.999... = 1 Why using complicated stuff like ∑ when you can prove it with simple numbers.
Dong Ninja	Posted - 2009.05.08 06:17:00 - [11] Using ∑ makes you look smart. See you gotta give concepts fancy names and formulas to go with them, or else the mathematician stop being the mathematician because everyone else knows how to do it, and we can't have that or people will start thinking they're smart. Originally by: Xen Gin Indeed, upgrading an MS OS is like taking a **** into a cake mixture, then complaining that it doesn't taste good when it's all done.
Giggles McHappypants	Posted - 2009.05.08 06:32:00 - [12] Originally by: Hobgoblin ll Proof: Let n = 0.999... Then 10n = 9.99... 10n - n = 9.999... - 0.999... 9n = 9.000... 9n = 9 n = 9/9 = 1 Holy crap u suck at math....10n - n = 9.999 is wrong...you dont subtract the "n" away, you would have to divide it away
Kulmid Asshats and Alcoholics Turbo.	Posted - 2009.05.08 06:41:00 - [13] Originally by: Hobgoblin ll Originally by: Lance Fighter 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. the proof makes perfect sense, as long as you assume that 0.99... is a number, that when subtracted from itself, gives you 0.. which.. um.. it does. This. Can be easy proven with fractions aswell: 0.111... = 1/9 9x 0.111... = 9 x (1/9) = 9/9 = 1 therefore 0.999... = 1 Why using complicated stuff like ∑ when you can prove it with simple numbers. This is a bit more shady than the OPs example because you are using fractions which are exact and using a repeating decimal that is not. _________________
Nomakai Delateriel Amarr Ammatar Free Corps	Posted - 2009.05.08 06:46:00 - [14] Also completely ignoring the fact that 9n in this example ISN'T 9. It's 8.999... Or you're rounding off numbers. ______________________________________________ -My respect can not be won, only lost. It's given freely and only grudgingly withdrawn.
Kulmid Asshats and Alcoholics Turbo.	Posted - 2009.05.08 07:32:00 - [15] Originally by: Nomakai Delateriel Also completely ignoring the fact that 9n in this example ISN'T 9. It's 8.999... Or you're rounding off numbers. Exactly... (10)(.999...) = 9.9999... (9)(.999...) = 8.9999... but yet (10)(.999...)-(.999...) = 9.000... _________________
Nomakai Delateriel Amarr Ammatar Free Corps	Posted - 2009.05.08 07:45:00 - [16] Originally by: Kulmid Originally by: Nomakai Delateriel Also completely ignoring the fact that 9n in this example ISN'T 9. It's 8.999... Or you're rounding off numbers. Exactly... (10)(.999...) = 9.9999... (9)(.999...) = 8.9999... but yet (10)(.999...)-(.999...) = 9.000... No. Because it's still 8.999... Otherwise you're rounding off. ______________________________________________ -My respect can not be won, only lost. It's given freely and only grudgingly withdrawn.
HankMurphy Minmatar Pelennor Enterprises	Posted - 2009.05.08 07:49:00 - [17] OP, it is neither a fact nor is it very interesting \o/ math fail threads ---------- Hey, sewer rat may taste like pumpkin pie, but I'd never know 'cause I wouldn't eat the filthy motherf***er.
Shadow Devourer	Posted - 2009.05.08 07:59:00 - [18] The answer involves a plane and a treadmill.
Fi Vantage Minmatar New Ligion	Posted - 2009.05.08 08:07:00 - [19] Edited by: Fi Vantage on 08/05/2009 08:08:30 Contributing to the fail! OP's proof is good enough. Wikipedia says so! I prefer using the infinite series version myself. Edit: Originally by: Shadow Devourer The answer involves a plane and a treadmill.
KingsGambit Caldari Knights	Posted - 2009.05.08 08:19:00 - [20] Originally by: Hobgoblin ll Let n = 0.999... Then 9n = 9.000... Ummmm...no. -------------
Akita T Caldari Navy Volunteer Task Force	Posted - 2009.05.08 08:48:00 - [21] The first thing you need to realize is that 0.99999999[...]9999999 is not an ACTUAL number. After that, it gets really, really easy. Want different proof ? Here's one. 1/9 = 0.111111[...]1111111 (1/9)*9 = 1 hence, 0.999999[...]9999 = 1 Tada ! EVE issues\|Mining revamp\|Build stuff\|Make ISK
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.08 09:16:00 - [22] Yay. Unlike the other "Interesting fact" thread, the OP has done it right. ____________________
Nomakai Delateriel Amarr Ammatar Free Corps	Posted - 2009.05.08 10:37:00 - [23] Depends on if you retain cardinal rankings of numbers approaching infinity (in some manner). Because if n= 0.99999 and 10n-0.999999 = 9 then if we replace the last 0.999999 in "10n-.99999 = 9" with f, then f is [1-[9x[1-n]]]. Still 0.99999, but with cardinal rankings it's still a number where f=<n. ______________________________________________ -My respect can not be won, only lost. It's given freely and only grudgingly withdrawn.
Malvaceae Veri	Posted - 2009.05.08 11:46:00 - [24] ITT: non-math guys learning the basics of infinite series.
Yakia TovilToba Halliburton Inc.	Posted - 2009.05.08 12:10:00 - [25] Edited by: Yakia TovilToba on 08/05/2009 12:13:26 Originally by: Nomakai Delateriel Originally by: Kulmid Originally by: Nomakai Delateriel Also completely ignoring the fact that 9n in this example ISN'T 9. It's 8.999... Or you're rounding off numbers. Exactly... (10)(.999...) = 9.9999... (9)(.999...) = 8.9999... but yet (10)(.999...)-(.999...) = 9.000... No. Because it's still 8.999... Otherwise you're rounding off. Dude, i found your last maths test: Linkage
jason hill Caldari Clan Shadow Wolf Sylph Alliance	Posted - 2009.05.08 13:03:00 - [26] errr destroy everything you touch
TimMc Gallente Brutal Deliverance Blackguard Coalition	Posted - 2009.05.08 13:07:00 - [27] Rounding ftl. I've had maths teachers try similar mind****s.
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.08 14:24:00 - [28] Originally by: Nomakai Delateriel Originally by: Kulmid Originally by: Nomakai Delateriel Also completely ignoring the fact that 9n in this example ISN'T 9. It's 8.999... Or you're rounding off numbers. Exactly... (10)(.999...) = 9.9999... (9)(.999...) = 8.9999... but yet (10)(.999...)-(.999...) = 9.000... No. Because it's still 8.999... Otherwise you're rounding off. Clearly wrong. 9n = 10n - n = 9.99999999... - 0.999999999999... = 9. You're making the classic mistake of thinking there's an infinityeth decimal place. ____________________
Jim McGregor	Posted - 2009.05.08 15:25:00 - [29] You get born on this planet and you spend your time doing this... --- Originally by: Roguehalo Can you nano Titans?
Micheal Dietrich Caldari	Posted - 2009.05.08 15:38:00 - [30] Man you people are so technical. I just round to the nearest.
Kazuo Ishiguro House of Marbles Zzz	Posted - 2009.05.08 16:50:00 - [31] Originally by: Akita T The first thing you need to realize is that 0.99999999[...]9999999 is not an ACTUAL number. After that, it gets really, really easy. It's a perfectly good number, although there are certainly more compact means of expressing it. It's just as well-defined as something like sqrt 2, which also happens to have an infinite decimal expansion. Quote: Want different proof ? Here's one. 1/9 = 0.111111[...]1111111 (1/9)*9 = 1 hence, 0.999999[...]9999 = 1 Tada ! For that to be valid, I'd also require you to prove your initial assertion that 1/9 = 0.1... 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. --- 20:1 mineral compression ISRC Racing, Season 7 - schedule
Intense Thinker Minmatar	Posted - 2009.05.08 17:21:00 - [32] The answer is 42 Pomp FTW!!!
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.08 19:52:00 - [33] Originally by: Kazuo Ishiguro Originally by: Akita T The first thing you need to realize is that 0.99999999[...]9999999 is not an ACTUAL number. After that, it gets really, really easy. It's a perfectly good number, although there are certainly more compact means of expressing it. It's just as well-defined as something like sqrt 2, which also happens to have an infinite decimal expansion. Quote: Want different proof ? Here's one. 1/9 = 0.111111[...]1111111 (1/9)*9 = 1 hence, 0.999999[...]9999 = 1 Tada ! For that to be valid, I'd also require you to prove your initial assertion that 1/9 = 0.1... 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. Actually, the argument in the OP is a proof that it IS convergent, specifically that it converges to 1. ____________________
Kazuo Ishiguro House of Marbles Zzz	Posted - 2009.05.08 20:17:00 - [34] At the 10n - n step, he has to make the assumption that the 0.999... part of 9.99... is convergent. Therefore it doesn't constitute proof of convergence. --- 20:1 mineral compression ISRC Racing, Season 7 - schedule
Taedrin Gallente Golden Mechanization Protectorate	Posted - 2009.05.08 21:09:00 - [35] Originally by: Kazuo Ishiguro At the 10n - n step, he has to make the assumption that the 0.999... part of 9.99... is convergent. Therefore it doesn't constitute proof of convergence. Which is why you convert the number into an infinite series and then do end behavior analysis to determine the value that it converges too
FOl2TY8 Tribal Liberation Force	Posted - 2009.05.09 01:05:00 - [36] Originally by: Taedrin x lim x->inf ∑ 9/(10^x) = 1 1 I have no idea what this means. I do however know how to be mean to a chick and still get laid. ---------- This post brought to you by the worst PVP'er in Eve
Leviathan Brian Amarr	Posted - 2009.05.09 01:23:00 - [37] I wonder what it's like wanting to be smarter than you actually are.
Evthron Macyntire	Posted - 2009.05.09 03:16:00 - [38] Let's see. 1 = whole number .999~ = fraction 9/9 = 1 = whole number 1/9 = .111~ = fraction I thought whole numbers were not fractions, even if the difference is infinitely small. I know some people like to use the excuse that 1/9 = .111~ 2/9 = .222~ ... 9/9 = .999~ But 9/9 would be reduced to 1, which is a whole number, which .999 is not. Oh wells. ------------------------------ Sigs like this.
Atama Cardel Perkone	Posted - 2009.05.09 03:16:00 - [39] Originally by: Nomakai Delateriel Also completely ignoring the fact that 9n in this example ISN'T 9. It's 8.999... Or you're rounding off numbers. No, you're just not following his proof exactly
Evthron Macyntire	Posted - 2009.05.09 03:17:00 - [40] Originally by: Evthron Macyntire Let's see. 1 = whole number .999~ = fraction 9/9 = 1 = whole number 1/9 = .111~ = fraction I thought whole numbers were not fractions, even if the difference is infinitely small. I know some people like to use the excuse that 1/9 = .111~ 2/9 = .222~ ... 9/9 = .999~ But 9/9 would be reduced to 1, which is a whole number, which .999 is not. Oh wells. This isn't elementary school STUPID! This is somewhere past highschool were logic doesn't apply. Some people are just idiots. ------------------------------ Sigs like this.
Taedrin Gallente Golden Mechanization Protectorate	Posted - 2009.05.09 03:44:00 - [41] Originally by: FOl2TY8 Originally by: Taedrin x lim x->inf ∑ 9/(10^x) = 1 1 I have no idea what this means. I do however know how to be mean to a chick and still get laid. It means 9/10 + 9/100 + 9/1,000 + 9/10,000 + 9/100,000 and then take the limit of this pattern as you continue to infinity. You will notice that 9/10 + 9/100 + 9/1,000 + ... is similar to .99999999..., if not exactly the same. Essentially, it is the mathematically correct way to say that for every 9 that you add to the end of .9999999999..., you get a little bit closer to 1. If you take this to infinity, the asymptote is 1.
Gara Al'Malik	Posted - 2009.05.12 13:47:00 - [42] Another proof that 0.999... = 1. Suppose that 0.999... < 1. Now there exists e > 0 such that 0.999... + e = 1. Let's write e in the decimal form e_1,e_2e_3e_4... Since e > 0, e_i > 0 for some i. However in decimal place i, 0.999... has 9 and so the sum 0.999... + e > 1, which is a contradiction. So now we know that 0.999... >= 1. Similarly we can rule out 0.999... > 1. The only possibility is then that 0.999... = 1
Reven Cordelle Caldari Yamainu-Mirai Heavy Industries	Posted - 2009.05.12 14:02:00 - [43] 0.999... will equal 1 if you round up a little. Simple really. :3
Taedrin Gallente Golden Mechanization Protectorate	Posted - 2009.05.12 15:21:00 - [44] Originally by: Gara Al'Malik Another proof that 0.999... = 1. Suppose that 0.999... < 1. Now there exists e > 0 such that 0.999... + e = 1. Let's write e in the decimal form e_1,e_2e_3e_4... Since e > 0, e_i > 0 for some i. However in decimal place i, 0.999... has 9 and so the sum 0.999... + e > 1, which is a contradiction. So now we know that 0.999... >= 1. Similarly we can rule out 0.999... > 1. The only possibility is then that 0.999... = 1 OOOOOO - nice proof.
Whitehound	Posted - 2009.05.12 15:26:00 - [45] 0.999... is not the same as 1, but only equal to it. The difference is the notation. Math puts a large emphasis on how you word it. The proof is ugly, because it defines n as 0.999... right at the start. This one is more elaborate and less twisted: 1/9 = 0.1 (= 0.111...) <=> 9 * 1/9 = 1/9 + 1/9 + ... + 1/9 <=> 9 * 1/9 = 0.1 + 0.1 + ... + 0.1 <=> 9 * 1/9 = 0.9 <=> 9/9 = 0.9 <=> 1 = 0.9 -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
Yakoff Alcatraz Inc. THE INTERSTELLAR FOUNDRY	Posted - 2009.05.12 17:49:00 - [46] What if, c - a - t, really spelt DOG. ___ It deosnt mttaer waht oredr the ltteers in a wrod are, olny taht the frist and lsat leettr be in the rghit pclae. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef.
Whitehound	Posted - 2009.05.12 18:03:00 - [47] Originally by: Yakoff What if, c - a - t, really spelt DOG. You would still manage to make a fool of yourself. -- 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 - 2009.05.12 18:16:00 - [48] Originally by: Whitehound Edited by: Whitehound on 12/05/2009 15:35:20 0.999... is not the same as 1, but only equal to it. The difference is the notation. Math puts a large emphasis on how you word it. The proof is ugly, because it defines n as 0.999... right at the start. This one is more elaborate and less twisted: Let 1/9 = 0.1 (= 0.111...) 9 * 1/9 = 1/9 + 1/9 + ... + 1/9 <=> 9 * 1/9 = 0.1 + 0.1 + ... + 0.1 <=> 9 * 1/9 = 0.9 <=> 9/9 = 0.9 <=> 1 = 0.9 You're assuming 9*1/9 is equal to 1. But you've defined 1/9 to be this number 0.111111111111111111111111111... rather than the number 1 divided by the number 9. It's correct, but you have to prove it. ____________________
Whitehound	Posted - 2009.05.12 18:35:00 - [49] Edited by: Whitehound on 12/05/2009 18:43:03 Originally by: ReaperOfSly You're assuming 91/9 is equal to 1. But you've defined 1/9 to be this number 0.111111111111111111111111111... rather than the number 1 divided by the number 9. It's correct, but you have to prove it. No. I did not assume, but I know that it is. And you do, too, btw. My proof is fine, you are just being stupid again. -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.*
xHazzarDx Roevhuller i Rummet	Posted - 2009.05.12 22:10:00 - [50] All this doesnt really matter.. it has allready been proven that the bird is equal to or greater than the word..
Eternal Error Exitus Acta Probant	Posted - 2009.05.12 22:29:00 - [51] Well I didn't read the OP, so I don't know if HIS proof is right. But .99999.... =1, in terms of currently defined mathematics.
Alena Lemming	Posted - 2009.05.13 21:55:00 - [52] Originally by: goodby4u I dont like these threads, they make me feel stupid. Quiet right, if it don't have a red crossy thing on it, and when i press fire something falls off my ship and make the red crossy thing go away then its not relevant to my situation. Now lets get back to something more important, Pron & shooting things..... nuff said!
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.13 22:15:00 - [53] Originally by: Whitehound Edited by: Whitehound on 12/05/2009 18:43:03 Originally by: ReaperOfSly You're assuming 91/9 is equal to 1. But you've defined 1/9 to be this number 0.111111111111111111111111111... rather than the number 1 divided by the number 9. It's correct, but you have to prove it. No. I did not assume, but I know that it is. And you do, too, btw. My proof is fine, you are just being stupid again. I'm not being stupid (and wtf do you mean "again"?), I'm being rigorous. You're treating 1/9 as a quantity entirely separate from the number 9. You may as well have named it n. Setting n = 0.1111111111111... and then asserting that 9n = 1. Which is pretty much what we're trying to prove in the first place. Seeing how the rest of your proof goes into similar detail, it seems odd that you would miss this. ____________________
Whitehound	Posted - 2009.05.14 14:15:00 - [54] Edited by: Whitehound on 14/05/2009 14:15:32 Originally by: ReaperOfSly I'm not being stupid (and wtf do you mean "again"?), I'm being rigorous. "1/9" is not a quantity but an expression made out of two elements and an operator. And yes, you are being stupid and you show it repeatedly here on the forum, which is why I say you are doing it again. Your problem is that you fail to accept what you already know and so you end up questioning what you know. If this is not stupid then what is? If you are into philosophy rather than mathematics then perhaps say so. It seems to be the case. Socrates already knew "I know that I know nothing." Fly save! -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
Michayel Lyon Gallente Mercantile Exchange	Posted - 2009.05.14 16:01:00 - [55] Oh my, there's a lot of stupid people out there... OP is correct. 0.999... is arbitrarily close to 1, which means that for any any number e < 1 (no matter how close to 1), 0.999... will always be closer. In layman's terms, you can't tell the difference between 1 and 0.999..., therefore they can be considered equal. The proof in the OP shows that 0.999... and 1 is, in fact, equal. --- Lasiverin Dark > Is everyone here allied? Red Knight > we are allied by our zombie like ability to ***** missions GM Xamother: "Beeing online is not considered harassment or exploit."
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.14 17:04:00 - [56] Edited by: ReaperOfSly on 14/05/2009 17:06:47 Originally by: Whitehound Edited by: Whitehound on 14/05/2009 14:15:32 Originally by: ReaperOfSly I'm not being stupid (and wtf do you mean "again"?), I'm being rigorous. "1/9" is not a quantity but an expression made out of two elements and an operator. And yes, you are being stupid and you show it repeatedly here on the forum, which is why I say you are doing it again. Your problem is that you fail to accept what you already know and so you end up questioning what you know. If this is not stupid then what is? If you are into philosophy rather than mathematics then perhaps say so. It seems to be the case. Socrates already knew "I know that I know nothing." Fly save! 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. And this IS maths. I am very much into maths. If it looks to you like philosophy, consider that there's a very good reason people say maths and philosophy are closely related. ____________________
The AEther Caldari Agony Unleashed	Posted - 2009.05.14 17:54:00 - [57] Originally by: Shadow Devourer The answer involves a plane and a treadmill. 1 plane and 0.9999...treadmill to be precise
TheEndofTheWorld Republic Military School	Posted - 2009.05.14 17:57:00 - [58] Edited by: TheEndofTheWorld on 14/05/2009 17:57:06 Originally by: ReaperOfSly Edited by: ReaperOfSly on 14/05/2009 17:06:47 Originally by: Whitehound Edited by: Whitehound on 14/05/2009 14:15:32 Originally by: ReaperOfSly I'm not being stupid (and wtf do you mean "again"?), I'm being rigorous. "1/9" is not a quantity but an expression made out of two elements and an operator. And yes, you are being stupid and you show it repeatedly here on the forum, which is why I say you are doing it again. Your problem is that you fail to accept what you already know and so you end up questioning what you know. If this is not stupid then what is? If you are into philosophy rather than mathematics then perhaps say so. It seems to be the case. Socrates already knew "I know that I know nothing." Fly save! 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. And this IS maths. I am very much into maths. If it looks to you like philosophy, consider that there's a very good reason people say maths and philosophy are closely related. Let's cut this short and ask it already. What is the point of life? (no, i don't mean it in a bad way )
ReaperOfSly Gallente Zetsubou Corp	Posted - 2009.05.14 18:57:00 - [59] Originally by: TheEndofTheWorld Edited by: TheEndofTheWorld on 14/05/2009 17:57:06 Originally by: ReaperOfSly Edited by: ReaperOfSly on 14/05/2009 17:06:47 Originally by: Whitehound Edited by: Whitehound on 14/05/2009 14:15:32 Originally by: ReaperOfSly I'm not being stupid (and wtf do you mean "again"?), I'm being rigorous. "1/9" is not a quantity but an expression made out of two elements and an operator. And yes, you are being stupid and you show it repeatedly here on the forum, which is why I say you are doing it again. Your problem is that you fail to accept what you already know and so you end up questioning what you know. If this is not stupid then what is? If you are into philosophy rather than mathematics then perhaps say so. It seems to be the case. Socrates already knew "I know that I know nothing." Fly save! 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. And this IS maths. I am very much into maths. If it looks to you like philosophy, consider that there's a very good reason people say maths and philosophy are closely related. Let's cut this short and ask it already. What is the point of life? (no, i don't mean it in a bad way ) 39. It used to be 42, but there's a recession on. ____________________
Whitehound	Posted - 2009.05.15 11:17:00 - [60] 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. -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.
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. ____________________
Whitehound	Posted - 2009.05.19 15:39:00 - [91] Originally by: ReaperOfSly 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. If you do not know what mathematics is about then just look it up in Wikipedia or any other encyclopedia. -- 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 16:40:00 - [92] Originally by: Whitehound Originally by: ReaperOfSly 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. If you do not know what mathematics is about then just look it up in Wikipedia or any other encyclopedia. It takes somewhat more than a visit to wikipedia to appreciate a vast topic like maths. ____________________
Wired Caldari Provisions	Posted - 2009.05.19 19:10:00 - [93] Why do all the hard work when there is somethign out there to do it for you. Proof ============================================= My sig got edited, and all i got was a lousy e-mail
Whitehound	Posted - 2009.05.19 19:32:00 - [94] Originally by: Wired Why do all the hard work when there is somethign out there to do it for you. Proof 0.999=1 => false 0.9999=1 => false 0.99999=1 => false 0.999999=1 => true 0.9999999=1 => true 0.99999999=1 => true That is why you do the hard work. -- If there is anything in your life you fear of losing, then keep your mouth shut once in a while.

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