0.999... = 1 - General - Facepunch Forum

[QUOTE=MountainWatcher;35302115]For there to be continuity, don't we need numbers to be infinitely close?[/QUOTE] The fact that numbers are infinitely closely packed in the real line is exactly why you can't pick a number adjacent to another number. [editline]26th March 2012[/editline] Definitions for continuity are carefully chosen so that they rely only on finite numbers.

Isn't this just proving that our ways of thinking are broken rather than making sense? If you pour a glass of water into 3 glasses with exactly the same amount in the 3 glasses, it's 1 glass devided in 3. Saying it's 1/3 is fine, but saying it's 33, etc % is wrong. Just because we can't devide 1 into 3 efficiently doesn't mean it's content is 0,9. Assuming that this flaw makes it right to say 0,9 is actually also 1, is just as flawed or even worse. Besides, 0,999 is infinitely far away from being 1. Just because infinity isn't a number doesn't mean it's not there. And even if it was a number, it can never become something between 0,999 and 1 unless you make up some new rules. But yeah i am probably too dumb for this with my elementary level math.

[QUOTE=shill le 2nd;35304589]0.111... = 1/9 0.222... = 2/9 0.333... = 3/9 0.444... = 4/9 0.555... = 5/9 0.666... = 6/9 0.777... = 7/9 0.888... = 8/9 0.999... = 9/9 = 1 end of thread[/QUOTE] watch as people argue that your logic is flawed and that you are stupid

Well, I don't mean picking a number just like that. I can't say how it looks like or write it, I can only say it's infinitely close to a number. but if that means the difference is 0, then it is the number itself. So doesn't it form an infinitesimal gap?

[QUOTE=MountainWatcher;35305807]Well, I don't mean picking a number just like that. I can't say how it looks like or write it, I can only say it's infinitely close to a number. but if that means the difference is 0, then it is the number itself. So doesn't it form an infinitesimal gap?[/QUOTE] I am confused.

Never mind, it's a bad argument.

[QUOTE=peepin;35293169]I fucking hate this equation bullshit: [i]x = 0.999... 10x = 9.999... 10x - x = 9.999... - 0.999... (or 10x - 0.999... = 9.999 - 0.999) 9x = 9 x = 1[/i] You have to be retarded to believe that. Seriously? Do you see the flaw? One of the biggest flaws: [i]x[/i] = 0.999... ! SO WHY ARE YOU SOLVING FOR [i]x[/i]?! Ok, lets forget that big flaw.. If [i]x[/i] = 0.999 step 3 would look like (9.999... = 9.999...) ; when we subtract [i]x[/i] (0.999) it will be 9 = 9! GENIUS! The other two are true.. Specially the blue one.[/QUOTE] Euler is rotating so fast in his grave that I believe we could use it to power Switzerland for the next few decades.

[QUOTE=sami-pso;35305796]Isn't this just proving that our ways of thinking are broken rather than making sense? If you pour a glass of water into 3 glasses with exactly the same amount in the 3 glasses, it's 1 glass devided in 3. Saying it's 1/3 is fine, but saying it's 33, etc % is wrong. Just because we can't devide 1 into 3 efficiently doesn't mean it's content is 0,9. Assuming that this flaw makes it right to say 0,9 is actually also 1, is just as flawed or even worse. Besides, 0,999 is infinitely far away from being 1. Just because infinity isn't a number doesn't mean it's not there. And even if it was a number, it can never become something between 0,999 and 1 unless you make up some new rules. But yeah i am probably too dumb for this with my elementary level math.[/QUOTE] Nobody here is talking about 0.999 but you. We're talking about 0.9... If you pour a glass of water into 3 glasses with exactly the same amount in the 3 glasses it's 1 glass divided in 3. So there is 1/3 in each. 1/3 = 0.3... Multiply it by 3 and you get 0.9... which is everything you had, which is 1. 1 = 3/3 = 1/3+1/3+1/3 = 0.3...+0.3...+0.3... = 0.3... x 3 = 0.9... These are all equal.

[QUOTE=J!NX;35305802]watch as people argue that your logic is flawed and that you are stupid[/QUOTE] duuuude its not 1 its smaller than one CANT YOU SEE THE FUCKING 9!

[url]http://www.wolframalpha.com/input/?i=0.9...[/url] [url]http://www.wolframalpha.com/input/?i=1%2F3[/url] [url]http://www.wolframalpha.com/input/?i=1%2F3*3&dataset=[/url] In wolframAlpha we trust.

[QUOTE=JohnnyOnFlame;35306951][url]http://www.wolframalpha.com/input/?i=0.9[/url]... [url]http://www.wolframalpha.com/input/?i=1%2F3[/url] [url]http://www.wolframalpha.com/input/?i=1%2F3*3&dataset=[/url] In wolframAlpha we trust.[/QUOTE] [url]http://www.wolframalpha.com/input/?i=0.9[/url]... [editline]26th March 2012[/editline] ahaha the link doesnt want to put the ellipses in so we are getting 9/10

[QUOTE=JohnnyOnFlame;35306951][url]http://www.wolframalpha.com/input/?i=0.9[/url]... [url]http://www.wolframalpha.com/input/?i=1%2F3[/url] [url]http://www.wolframalpha.com/input/?i=1%2F3*3&dataset=[/url] In wolframAlpha we trust.[/QUOTE] [url]http://www.wolframalpha.com/input/?i=0.99999999999999+repeating[/url] 1st one broke

I only watched this to fap to the sound of her voice.

My math teacher did so many proofs on this... Can we all just agree .999(Repeating) = 1.

[QUOTE=MountainWatcher;35303207]Middle can be any digit that is infinitely far away from the extremities of the number, the argument stays the same. Let's take a semi-line if you prefer. It has a defined start but stretches to infinity. if you place the origin of your referential on infinity, the origin of the line will be located at infinity, but it will still be there, it'll exist. Not in a finite distance, but it'll be there.[/QUOTE] There is no definable 'middle' to an infinite string of numbers, but your second point is interesting. An infinite line is, in every possible way a person might care about, [i]equivalent[/i] to a circle, with the north pole representing the point at infinity. So we can define various properties at infinity for 'things' (functions, etc) acting on the real numbers by the way those functions act on circles at the north pole. But this isn't relevant. [QUOTE=PederPauline;35303885]I didn't say their evidence was faulty. You can come up with advanced mathematical ways of showing 0.999... = 1, but all they're really showing is that we don't allow for infinitely small numbers in math.[/QUOTE] No one's sitting around saying 'I won't allow for infinttesimals!'. Their non-existence is a direct consequence of our definition of the real numbers, which is what you happily use everyday without question. [QUOTE=MountainWatcher;35305807]Well, I don't mean picking a number just like that. I can't say how it looks like or write it, I can only say it's infinitely close to a number. but if that means the difference is 0, then it is the number itself. So doesn't it form an infinitesimal gap?[/QUOTE] Choose two distinct numbers [i]a[/i] and [I]b[/I]. The difference between them is ([I]a-b[/I])/2. This is non-zero since [I]a[/I] and [I]b[/I] are distinct. Moreover, the difference is [I]definable[/I] as long as they are distinct--it may be very small, but it is definable [I]no matter how close they are together[/I]--and 0 if and only if they are in fact the same number. So what is the difference between 0.999... and 1?

[IMG]http://i.imgur.com/b7GHL.jpg[/IMG]

[QUOTE=areolop;35307692]My math teacher did so many proofs on this... Can we all just agree .999(Repeating) = 1.[/QUOTE] nope because apparently people don't know what repeating decimals [I]are[/I], to begin with

[QUOTE=Silly Sil;35306296]Nobody here is talking about 0.999 but you. We're talking about 0.9... If you pour a glass of water into 3 glasses with exactly the same amount in the 3 glasses it's 1 glass divided in 3. So there is 1/3 in each. 1/3 = 0.3... Multiply it by 3 and you get 0.9... which is everything you had, which is 1. 1 = 3/3 = 1/3+1/3+1/3 = 0.3...+0.3...+0.3... = 0.3... x 3 = 0.9... These are all equal.[/QUOTE] Yes and you lose 0.1 making it impossible for it to be 1 again.

My brother told me another way to think about it. What is 1 minus 0.9... The answer is 0.0... That is a fancy way of saying zero. So if 1-0.9... is 0 they must be the same value.

[QUOTE=yawmwen;35308284]My brother told me another way to think about it. What is 1 minus 0.9... The answer is 0.0... That is a fancy way of saying zero. So if 1-0.9... is 0 they must be the same value.[/QUOTE] No, you're just going to have the idiots saying that it equals "0.0...1" which makes no sense.

[QUOTE=sami-pso;35308256]Yes and you lose 0.1 making it impossible for it to be 1 again.[/QUOTE] What in Sagan's name are you blathering about 0.9... =/= 0.9

[QUOTE=sealclubber;35307709]There is no definable 'middle' to an infinite string of numbers, but your second point is interesting. An infinite line is, in every possible way a person might care about, [i]equivalent[/i] to a circle, with the north pole representing the point at infinity. So we can define various properties at infinity for 'things' (functions, etc) acting on the real numbers by the way those functions act on circles at the north pole. But this isn't relevant. No one's sitting around saying 'I won't allow for infinttesimals!'. Their non-existence is a direct consequence of our definition of the real numbers, which is what you happily use everyday without question. Choose two distinct numbers [i]a[/i] and [I]b[/I]. The difference between them is ([I]a-b[/I])/2. This is non-zero since [I]a[/I] and [I]b[/I] are distinct. Moreover, the difference is [I]definable[/I] as long as they are distinct--it may be very small, but it is definable [I]no matter how close they are together[/I]--and 0 if and only if they are in fact the same number. So what is the difference between 0.999... and 1?[/QUOTE] I don't understand your point regarding the circles. Also, do you have anything to say about how the probability of guessing the same specific number in a number line as someone else is 0? I understand statistic accepts this result, but if my chance of picking a certain number is 0, then it's impossible for me to pick any number.

[QUOTE=shill le 2nd;35308327]No, you're just going to have the idiots saying that it equals "0.0...1" which makes no sense.[/QUOTE] As long as the 9 repeats indefinitely so does the 0. If the 9 had a definite end, then a 1 would eventually pop up.

This is why engineering is better, we just round numbers to 3 significant figures and leave it at that.

[QUOTE=MountainWatcher;35308438]I don't understand your point regarding the circles. Also, do you have anything to say about how the probability of guessing the same specific number in a number line as someone else is 0? I understand statistic accepts this result, but if my chance of picking a certain number is 0, then it's impossible for me to pick any number.[/QUOTE] I'll never pick your number because you're a god damn cheater!

Im bad at math and whats going on here

[QUOTE=MILKE;35308582]Im bad at math and whats going on here[/QUOTE] A continuous debate of whether or not the endless decimal representation of 3/3 can be considered 1. Basics of one side: If 3/3 = 1, then .999999... = 1 Basics of other side: .9999999999... isn't 1. [B]Don't quote this. I'm not taking either side on the issue.[/B]

[img]http://i249.photobucket.com/albums/gg221/mooman1080/spongebob-math.gif[/img]

1-0.333...= A 0.333...*2= B A>B By an infinitely small number, we can just ignore it. The whole problem is that 1 cannot be properly divided by 3 and produce anything different than 1/3. 0.333... is just like a fancy nickname to 1/3 and not equal when a part of 1. But this is my view of the situation. Also who and why decided to prove something that is no way beneficial to anything everywhere. Just use something that suits you and doesn't bother you during calculations. Round numbers only when you write the result, keep the big numbers you work on to the calculator to remember. Have a nice day.

[QUOTE=Corey_Faure;35308633]A continuous debate of whether or not the endless decimal representation of 3/3 can be considered 1. Basics of one side: If 3/3 = 1, then .999999... = 1 Basics of other side: .9999999999... isn't 1.[/QUOTE] With the OP's logic, solving this algebraically: x/3 * 3 = x (x/3)*3 = (x)*3 x * 3 = x * 3 (x * 3)/3 = (x * 3)/3 x = x With this logic, any number you replace with x, theoretically, will always equate to be the same. For example, where x=2: 2/3 * 3 = 2 2/3 = 0.666 0.666 * 3 = 2 0.666 * 3 = 2/3 * 3 It's basically asking the question: "Is the fractional representation equivalent to that of its decimal form?" If that's the case, we should be able to do this with any number, as previously stated. 15/3 * 3 = 15 15/3 = 5 5 * 3 = 15 15/3 = 5 * 3 The only reason that it comes out to be 0.999... is because 1/3 is a repeating decimal and as winds up with odd decimal approximations such as 0.999.