0.999... = 1 - General - Facepunch Forum

[QUOTE=Bradyns;35292301]0.333..... is the decimal representation of the fraction (1/3). It's the same thing.[/QUOTE] no, the key word is there "representation" you'd need an infinite numbers of 3333s, and the more you'd have, the closer you'd get to 1 it's not the same thing, and that's why the whole 0.999 = 1 is BS

[QUOTE=Smashmaster;35293798]So do it.[/QUOTE] Would you agree with me that using the limit method that you showed to find the real value is an approximation, good for maybe an explanation in theory but not for a concrete answer? Using simple mathematical operations, if you were to subtract 0.9 to the infinity from 1, you wouldn't get 0 unless you're using an approximation of the value.

shitstorm successful

Its simple ... 1/3 is NOT 0.3333.. ; however, 0.3333... is an APPROXIMATION of 1/3 - it is CLOSE to it So doing 0.3333.. * 3 = 0.9999.. - Which is CLOSE to 1 - but its NOT 1! And doing 1/3 * 3 = 1 ; which is infact true!

[QUOTE=Plastical;35293774]the problem with the limit method is that it is an approximation of the answer for whatever value of n it is approaching.[/QUOTE] No it's not. lims give exact answers.

I remember there being another rule that applies to this which says that if there is no real number between two 'Numbers', they must be the same as there is literally nothing between them.

[QUOTE=Plastical;35293931]if you were to subtract 0.9 to the infinity from 1, you wouldn't get 0 unless you're using an approximation of the value.[/QUOTE] Yes, you would. I think you don't really grasp the concept of infinity well.

[QUOTE=Glorbo;35293971]No it's not. lims give exact answers.[/QUOTE] It depends, in Smashmaster's example, it is one.

[QUOTE=Plastical;35294006]It depends, in Smashmaster's example, it is one.[/QUOTE] What I mean is, lims are never approximates. limits give you precise numbers, whether they are rational or irrational. You choose where to cut them into an approximate.

[QUOTE=Plastical;35293931]Would you agree with me that using the limit method that you showed to find the real value is an approximation, good for maybe an explanation in theory but not for a concrete answer? Using simple mathematical operations, if you were to subtract 0.9 to the infinity from 1, you wouldn't get 0 unless you're using an approximation of the value.[/QUOTE] I wouldn't. Saying there is a number infinitely close to 1, but not equal to 1, is a contradiction. It's like saying there is an object that is colored entirely red, and colored a little blue. You have to be careful when working with infinity. You can't round infinity, and you can't approximate infinity. If you multiply something by infinity, you get infinity. If you divide by it, you get zero. You don't get 'almost infinity' or 'almost zero.' That's just how it works.

[QUOTE=Smashmaster;35294053]I wouldn't. Saying there is a number infinitely close to 1, but not equal to 1, is a contradiction. It's like saying there is an object that is colored entirely red, and colored a little blue.[/QUOTE] The idea is that the limit value of 10^n as n [i]approaches[/i] -infinity [i]tends[/i] to 0. I get what you're saying with infinitely approaching 1, but if what you're saying is true, then if you start with 1 and you keep infinitely dividing by 2, you would eventually reach 0. I'm not so sure about that.

[QUOTE=Smashmaster;35294053]It's like saying there is an object that is colored entirely red, and colored a little blue.[/quote] That doesn't actually work, since that would mean saying there's a number that's exactly one, but isn't one. [quote]You have to be careful when working with infinity. You can't round infinity, and you can't approximate infinity.[/quote] You seem to be doing a fine job of it.

[QUOTE=MRTW113;35293954]shitstorm successful[/QUOTE] Caused by fucking decimals, no less.

[QUOTE=Gutsani;35293760]Good job being wrong 4 times in a single post. U just failed math.[/QUOTE] Good job being wrong two times in a single post. You just failed English. Besides, it was pretty obvious that I'd just made a couple of typos because I wasn't thinking straight. I'm not dumb enough to actually think that 9.999 recurring is equal to one, I meant 0.999 recurring, and accidentally put the number at the beginning instead of a zero. But whatever, this is obviously [I]really[/I] important to you all, so I'll just leave you guys to it.

[QUOTE=Plastical;35294105]if what you're saying is true, then if you start with 1 and you keep infinitely dividing by 2, you would eventually reach 0. I'm not so sure about that.[/QUOTE] I can prove that it does in 10 different ways. You can't prove that it doesn't in even 1 way. [QUOTE=Plastical;35294105]realistically speaking Infinity + 2 is greater than infinity although I would understand why you wouldn't accept this answer.[/QUOTE] ∞ + 2 > ∞ Undefined operation

[QUOTE=Plastical;35294105]The idea is that the limit value of 10^n as n [i]approaches[/i] -infinity [i]tends[/i] to 0.[/QUOTE] That's because you can't really get to infinity. Saying "I got to infinity" is contradicting yourself, because infinity is defined as a point that you cannot reach no matter how much you add and try. Now, in [b]theory[/b], if you could somehow jump to this magical point called infinity (by maybe advancing an infinite amount of steps at once), you would see that yes, it equals zero. My logic goes as this. If I have a chocolate bar, and I want to divide it to an infinite number of people, the only reasonable quantity I can give to anyone is zero, because if I gave any tangible amount, then it will eventually run out before I can divide it equally to everyone. I can't give them an infinitely small piece because it's the same as zero. 0.00000...001 is not infinitely small. Why? Because the fact that I just ended that number with a 1 contradicts my previous statement that it never ends. And if it never ends, then there can't be a number like that. My point is, in order for anyone to get [b]some[/b] amount, you have to stick that one somewhere, but you can't, because you'll be contradicting yourself.

[QUOTE=Smashmaster;35294224]I can prove that it does in 10 different ways. You can't prove that it doesn't in even 1 way.[/QUOTE] Please do.

[QUOTE=Paramud;35294251]Please do.[/QUOTE] And while I work on this, would you please work on your definitive 0.999... =/= 1 proof as well? No? Then I'm not wasting my time.

-snip-

[QUOTE=Smashmaster;35294272]And while I work on this, would you please work on your definitive 0.999... =/= 1 proof as well? No? Then I'm not wasting my time.[/QUOTE] Educating a waste of time? Teachers everywhere are heartbroken. [QUOTE=Glorbo;35294238]My logic goes as this. If I have a chocolate bar, and I want to divide it to an infinite number of people, the only reasonable quantity I can give to anyone is zero, because if I gave any tangible amount, then it will eventually run out before I can divide it equally to everyone. I can't give them an infinitely small piece because it's the same as zero.[/QUOTE] Actually, you can't give them all a piece of chocolate because eventually you'll get to atoms and if you try to split those equally they'll all [b]die[/b].

[QUOTE=Plastical;35294280]Alright can you address what I wrote about one of your proofs then because I've yet to see a response to that.[/QUOTE] I would but that statement appears to be in agreement with my position. EDIT: And it doesn't "tend" to zero. It equals zero.

Jesus you people are dense. There are so many simple and valid proofs of this, it's insane to try to argue otherwise. [url]http://en.wikipedia.org/wiki/0.999...#Algebraic_proofs[/url]

Guys BRB I have to go to my annual moon landing conspiracy meeting And then I have to go prove that the Earth is flat, and that the sun revolves around it

[QUOTE=fenwick;35294312]it's insane to try to argue otherwise.[/QUOTE] I thought the point of having an interest in any sort of science was that you can argue against just about anything, no matter how widely accepted?

[QUOTE=Paramud;35294385]I thought the point of having an interest in any sort of science was that you can argue against just about anything, no matter how widely accepted?[/QUOTE] Nah dawg you've got it wrong. It's about evidence.

Filling up a glass with 1u of water into 3 glasses each holding .333u = 1u. Makes sense, then my brain goes no its .999u. Obviously the remaining water are those small droplets in the bottle.

[QUOTE=Paramud;35294385]I thought the point of having an interest in any sort of science was that you can argue against just about anything, no matter how widely accepted?[/QUOTE] This isn't like that, do you know how proofs work? They prove things, inarguably. Can you point out a flaw in one of the proofs? No? Then they're right.

[QUOTE=Smashmaster;35294367]And then I have to go prove that the Earth is flat, and that the sun revolves around it[/QUOTE] Are you trying to say that burden of proof lies with the person with the negative claim? [QUOTE=fenwick;35294603]This isn't like that, do you know how proofs work? They prove things, inarguably. Can you point out a flaw in one of the proofs?[/QUOTE] (In response to your last question,) not particularly. Then again, I'm not a mathematician. I just thought that it'd make sense for someone to enjoy educating people on why they think what they think, especially if the other person disagrees with them.

[QUOTE=Paramud;35294605]Are you trying to say that burden of proof lies with the person with the negative claim?[/QUOTE] Uh... [b]YES[/b]? It lies on everyone who takes a position.

[QUOTE=Smashmaster;35294652]Uh... [b]YES[/b]? It lies on everyone who takes a position.[/QUOTE] Please, excuse me for the religious motivation of the image. I just don't feel like spending the time editing it to be more appropriate. [img]http://timcooley.files.wordpress.com/2009/12/christian-logic.jpg[/img]