Rablet Posted November 2, 2005 Share Posted November 2, 2005 whats 1/3 - .3333333.. whats 2/3 .6666666.... whats 1/3 + 2/3 .9999... (.6666+.3333=.9999) so .9999 = 1 586757464[/snapback] 2/3 = 0.666666...7 Link to comment Share on other sites More sharing options...
rob.derosa Posted November 2, 2005 Share Posted November 2, 2005 I'm not sure I like that page... those proofs make like 0.9r is an actual number - sorry, but it's not. It's a concept, not a number. You can't just transform the concept of infinity into a bunch of nines.From that page: 1 - 0.9999... = 0.0000... = 0 1 = 0 + 0.9999... = 0.9999... Huh? :wacko: Look @ Steps 1 - 2... 0.0r does not equal 0. :no: 586757451[/snapback] lok at the first step, its already assuming that 1 = 0.9999, its not proving anything, its just proving thats their assumption is true. lmao Link to comment Share on other sites More sharing options...
khaos34 Posted November 2, 2005 Share Posted November 2, 2005 lok at the first step, its already assuming that 1 = 0.9999, its not proving anything, its just proving thats their assumption is true. lmao 586757482[/snapback] haha yes, didn't notice that at first :yes: Link to comment Share on other sites More sharing options...
Brandon Posted November 2, 2005 Share Posted November 2, 2005 2/3 = 0.666666...7 586757481[/snapback] only if rounding Link to comment Share on other sites More sharing options...
Rablet Posted November 2, 2005 Share Posted November 2, 2005 only if rounding 586757501[/snapback] Yeah, you're right, I thought about it and realized I was wrong. :blush: Link to comment Share on other sites More sharing options...
Michael1406 Posted November 2, 2005 Share Posted November 2, 2005 I was gonna say that about the 1/3 thing! If 1/3 = 0.3r Then 3/3 = 0.9r But 3/3 = 1 So 0.9r = 1 Link to comment Share on other sites More sharing options...
lloydo Posted November 2, 2005 Share Posted November 2, 2005 what about how 0! = 1??? that ****es me off 586757477[/snapback] That's by construction, if 0! didn't equal 1 then all factorials wouldn't work. Link to comment Share on other sites More sharing options...
Sethos Posted November 2, 2005 Share Posted November 2, 2005 Oh, get laid! Link to comment Share on other sites More sharing options...
Smigit Posted November 2, 2005 Share Posted November 2, 2005 only if rounding 586757501[/snapback] yes but so is whats 1/3 - .3333333.. whats 2/3 .6666666.... whats 1/3 + 2/3 .9999... (.6666+.3333=.9999) so .9999 = 1 0.333..... != 1/3, as said its a representation. If you do maths you get told to use fractions where possible since they are precise where 0.333 isnt (not to mention it may imply rounding and be different to 1/3 altogether) saying that I always work in decimal.....take that maths teacher :D Link to comment Share on other sites More sharing options...
GrimReeper Posted November 2, 2005 Share Posted November 2, 2005 Its just a weird thing which is cool but sadly I doubt true. Sorry to hijack your thread but check this out. Its just like 1! (1 Factorial) is 1 and 0! (0 factorial) is 1. :o I forgot the reasoning behind it sorry. Link to comment Share on other sites More sharing options...
russ0943 Posted November 2, 2005 Share Posted November 2, 2005 The correct way to say this is that .9999.... is equal to 1 when it is infinitesimally close to one. Link to comment Share on other sites More sharing options...
khaos34 Posted November 2, 2005 Share Posted November 2, 2005 I was gonna say that about the 1/3 thing!If 1/3 = 0.3r Then 3/3 = 0.9r But 3/3 = 1 So 0.9r = 1 586757510[/snapback] Sorry, still doesn't work :) Look back a few posts. You can't multiply 0.3r by 3 and get 0.9r. Link to comment Share on other sites More sharing options...
romanr Posted November 2, 2005 Share Posted November 2, 2005 Let X = 0.99999...10X = 9.99999... 10X - X = 9.99999... - 0.99999... 9X = 9 X = 1 :pinch: 586757333[/snapback] That's dumb. You simply can't do that. 10X = 9.9999999999 is an equation which if you solve for X you get X = 9.9999999999/10 which means X = 0.99999999999 10X - X = 9.99999... - 0.99999... is a completely different equation which if you solve for X you get 10X - X = 9 9X = 9 X = 1 if your original equation is 10X = 9.9999999999 then 10X - X = 9.9999999999 - X, which would still yield a an answer of 0.9999999999 for X Link to comment Share on other sites More sharing options...
Smigit Posted November 2, 2005 Share Posted November 2, 2005 I love that site that got posted A rigorous analytical proof (relatively tough mathematics). . . . . I didn't understand that proof. But they proved it, too!The proof was fallacious. Send it to me and I'll show you why. so he puts up proofs on his own site he cant understand and then claims he will disect anyone elses proof. yeah right... furthermore Closer and closer? How can it be getting closer and closer? It's one number! THIS is a sequence which gets closer and closer to 1 but never reaches it:0.9 0.99 0.999 0.9999 0.99999 ... Whereas 0.9999... is just a SINGLE NUMBER which isn't even IN that sequence. (No, it's not "right at the end". The sequence goes on forever. That means it doesn't have an end.) You have to consider the entire number, all at once. Not little finite chunks. But look carefully. That sequence gets closer and closer to 1 but never reaches it: but it ALSO gets closer and closer to 0.9999... and never reaches it either! well it does reach it if you repeate that sequence an infinite amount of times. Link to comment Share on other sites More sharing options...
slang123 Posted November 2, 2005 Share Posted November 2, 2005 0.99999999.... is equal to 1. get over it. Its all to do with the definition of the real numbers, if they were not equal then there would be a number between them, which there isnt Link to comment Share on other sites More sharing options...
khaos34 Posted November 2, 2005 Share Posted November 2, 2005 0.99999999.... is equal to 1. get over it. Its all to do with the definition of the real numbers, if they were not equal then there would be a number between them, which there isnt 586757588[/snapback] Yes there is. There is infinity numbers between them. Link to comment Share on other sites More sharing options...
slang123 Posted November 2, 2005 Share Posted November 2, 2005 No, name one Link to comment Share on other sites More sharing options...
Rablet Posted November 2, 2005 Share Posted November 2, 2005 No, name one 586757599[/snapback] 1-0.99999999.... :p Link to comment Share on other sites More sharing options...
slang123 Posted November 2, 2005 Share Posted November 2, 2005 Thats not a number between 0.999999999999..... and 1 Link to comment Share on other sites More sharing options...
stfu. Posted November 2, 2005 Share Posted November 2, 2005 This should anwser the problem. 586757542[/snapback] Thanks for the trojan... Link to comment Share on other sites More sharing options...
lexor Posted November 2, 2005 Share Posted November 2, 2005 So for those who don't want to read the whole thing, 0.9999repeating = 1.000repeating because there is no interval separating them. Ok here is justificaiton for original problem: If we approximate a real number x = 0.a1a2...akak+1ak+2... between 0 and 1 with any number in an "approximating interval" [0.a1a2...ak , 0.a1a2...ak-1(ak + 1)], with rational "endpoints" both ending in an infinite sequence of zeros, that is, a1/101 + a2/102 + a3/103 + ... + ak/10k <= x <= a1/101 + a2/102 + a3/103 + ... + (ak + 1)/10k We know that an upper bound for the error of this approximation is "the right end point" minus "the left endpoint" = 1/10k. We will call the endpoints 0.a1a2...ak and 0.a1a2...ak-1(ak + 1) approximaters of x. So an approximater of the real number s is in fact a modification of s obtained by changing a tail end of s into a string of zeros. Rational numbers who end in a string of zeros are approximaters of themselves. If we accept that 0.999999... < 1.0000000... then this is contrary to a strong property of the real numbers: Between any two distinct real numbers s and t we can find disjoint approximating intervals of s and t which separate them. Here we can find no approximating intervals which separate 0.9999..... and 1.00000...... In order to preserve this property, we must accept the alternative, that is, that 0.999999... = 1.000000... And for the rest of you, take a Real Analysis course. Link to comment Share on other sites More sharing options...
khaos34 Posted November 2, 2005 Share Posted November 2, 2005 No, name one 586757599[/snapback] That's the thing I think some people are getting wrong... Another number between 0.9999... and 1 is 0.99999... - IF you're in the "everything is numbers" mindset. The thing is, 0.9999... is not a number in the first place, so how can there be a number between them? It's like saying "Tell me the number between orange and 1". Again, 0.9999... represents the concept of infinity, not a number. 0.999... is infinitly closer to 1, but it never touches it. This is the first thing you learn in Calculus. Link to comment Share on other sites More sharing options...
Gundamdriver Posted November 2, 2005 Share Posted November 2, 2005 You can find this by finding the sum of infinity (geometric sequence). 0.9999999999... can be represented by: 0.9 + 0.09 + 0.009 + ... The sum of infinity: (First term) / (1 - Common ratio) 0.9 / (1- 0.1) = 1 So, proved. Link to comment Share on other sites More sharing options...
slang123 Posted November 2, 2005 Share Posted November 2, 2005 Um.... I'm doing second year in a maths degree, and we spent alot of time defining the real numbers. I can tell you that 0.99999.... is a number, its the infinite decimal expansion of 1. It is equal to 1. Fact. You can keep arguing if you like, but you're never going to disprove that Link to comment Share on other sites More sharing options...
DomZ Posted November 2, 2005 Share Posted November 2, 2005 I'm gonna go give Einstein a call... Nah I personally think that 0.9999.... is approximately 1. It can never be 1, but seems as it goes on forever it basically is 1. I wouldnt say that 0.999.... is not 1 though. Link to comment Share on other sites More sharing options...
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