Does 0.9 repeated = 1?

[Kushna Mufeed]

Are you going to try to tell me that something infinitely close to 1 isn't 1?

[Ynot]

Are you going to try to tell me that something infinitely close to 1 isn't 1? yes

[Tamias.Squirrel]

Yes. EDIT: xD Ynot got to it first!

[Kushna Mufeed]

Prove it

[Ynot]

Prove it for practical examples, 0.9 recurring does equal 1, because machines have a fixed amount of space in which to store a value give it an irrational number like 0.9 recurring, and it'll fill up the space, and still have a remainder, so it'll round up to 1, but this is not accurate

[Merlock]

0.9 recurring is, by definition, a number that infinitely reaches towards 1 but never gets there. So that question really has no place. No one asks whether 1 equals to 2...we know that each is a different number by definition, as it were. So why ask whether 0.9 recurring (that very number) equals to 1 (a different number) if you've just spoken about two different numbers? Not variables but different real numbers. Just because it's used as equaling 1 for calculations doesn't make it precise and true. Sounds ridiculous but...you can't argue with the number's very definition, and apparently people prefer actually finishing their calculations rather than sitting there at a dead end unable to work with an irrational number that never ends. I hate math though, so I'm just going at this from a logical point of view. Definitions are axioms!

[Ynot]

another way to look at it 0.15 is a rational number but write that in hex, and you get 0x0.2666666..... an irrational number a rational number in one base can be irrational in another and vice versa there will likely be some base where decimal 0.9 recurring is rational and therefore easily shown that it is not equal to 1

[ninja9578]

another way to look at it 0.15 is a rational number but write that in hex, and you get 0x0.2666666..... an irrational number a rational number in one base can be irrational in another and vice versa there will likely be some base where decimal 0.9 recurring is rational and therefore easily shown that it is not equal to 1 I was going to say something like that.

[wendylove]

0.9 recurring is, by definition, a number that infinitely reaches towards 1 but never gets there. So that question really has no place. No one asks whether 1 equals to 2...we know that each is a different number by definition, as it were. So why ask whether 0.9 recurring (that very number) equals to 1 (a different number) if you've just spoken about two different numbers? Not variables but different real numbers. Just because it's used as equaling 1 for calculations doesn't make it precise and true. Sounds ridiculous but...you can't argue with the number's very definition, and apparently people prefer actually finishing their calculations rather than sitting there at a dead end unable to work with an irrational number that never ends. I hate math though, so I'm just going at this from a logical point of view. Definitions are axioms! Actually, you're wrong. Firstly, people have asked for a proof that 1 does not equal 2, and all the other stuff assumed in arithematic. 1=0.9999... http://en.wikipedia.org/wiki/0.999...#Proofs It has been proven, look above. Also, 0.9999.. by definition is not irrational. See 1/3=0.3333....., then you times it by 3/3=0.9999.... Actually, even if you couldn't do that it still has a repeating digit, which proves it can't be irrational, as the definition of a irrational number is that there is no repeating digit in sequences of numbers in n-1 turns. For example you don't get stuff like 2.12222..., this would have a repeating 2, so wouldn't be irrational. 0.999.. has repeating 9 so is not irrational. P.S. Seriously, don't do mathematics. there will likely be some base where decimal 0.9 recurring is rational and therefore easily shown that it is not equal to 1 It has been mathematically prove, look above. That 0.9999... =1, so its a fact or a theorem in this case.

[ninja9578]

Wrong. y = x^3 / x - 5(.999~) If 1 = .999~ then y would be undefined at x = 5. When x = 5, that equation equals -5. You have to use limits to show it, but it's -5, not undefined. Limits is a weird thing. Those proofs are correct on wiki, however you can also prove that they don't work. This happens a lot with limits and calculus.

[Ynot]

the (1/9) x 9 proof was proven inaccurate it's essentially using a property of mathematics to disprove that same property there's a counterpoint that says, it should be written as (I'm paraphrasing) (1 / 8.999999.....) x 8.99999..... which is not possible to do (with absolute accuracy) so 0.99999.... cannot equal 1

[wendylove]

Limits is a weird thing. Those proofs are correct on wiki, however you can also prove that they don't work. This happens a lot with limits and calculus. Proof doesn't work. Seriously, are you some sort of mathematical crank. A proof is a proof, it has been proven. It is a theorem, it is a fact. Anyway, the only thing strange is that Tom Apostol concludes, The fact that a real number might have two different decimal representations is merely a reflection of the fact that two different sets of real numbers can have the same supremum

[ninja9578]

The problem with numbers is that people look at them differently depending on how they are used. Not in terms of rounding, just in terms of how they get used in calculations. Does .999~ = 1? Computers - yes Physics - yes Relativity Physics - no Math - no Calculus - yes Does -0 = 0? (another common dispute) Computers - no Physics - no Relative Physics - no Math - yes Calculus - yes If you'd like I can give examples of all of these.

[wendylove]

it's essentially using a property of mathematics to disprove that same property there's a counterpoint that says, it should be written as (I'm paraphrasing) (1 / 8.999999.....) x 8.99999..... Firstly, NO. 9.99999=10, not that 8.999999=10. So lets 1/1=9/9, everything is okay, then we have 9x1/9=1, then we have 9x 0.111...=1, therefore 0.99999=1. Anything divide by something is 1, so how is that a counterpoint? Lastly, it has been prove by analysis, so there. Look at the bottom of the wiki article. Math - no Calculus - yes Calculus is mathematics, also you can use analysis to prove it. So what are you basing you're assumptions on. It has been proven in mathematics that 0.99999...=1. You can prove it using constructionism, which is most concrete form of mathematics. You can construct it from the real numbers, or prove it by dedekind cut.

[hungrymanz]

Wow, I used to think Ynot was an intelligent person. And here he is saying that .99... does not equal 1. It does. There are numerous proofs that .99... equals 1. How many proofs are there that it does NOT equal 1? Zero. There are no such counter-proofs. Here is a proof. Try to think of a number between .9999... and 1. Thought of a number? No? That's because there are no numbers between .999... and 1. You know why? Because they're the same number. If they were not, then there would be a number between them. This isn't rocket science. I've known this since middle school. http://polymathematics.typepad.com/p...sorry_it_.html One of many sites that you could learn from. PS: Please stop posting your flawed mathematics in this thread. It is an embarrassment. Ynot, stop posting here unless you cure your ignorance.

[ninja9578]

See my post above about multiple views. Computer science says that 1/∞ = 0 so 1 - 1/∞ = 1 Physics says the same thing because it uses limits to reach asymptotes Relative physics uses calculus which can reach asymptotes, but doing so causes failure among basic physics so the break down of physics is what says that .999~ != 1, not the math. Simple math states that asymptotes can not be reached, therefore .999~ != 1 Calculus can use limits to reach as asymptotes

[wendylove]

failure among basic physics so the break down of physics is what says that .999~ != 1, not the math. Simple math states that asymptotes can not be reached, therefore .999~ != 1 Calculus can use limits to reach as asymptotes Mathematics says you can do a dedekind cut and then show that 0.9999...=1. There is various mathematical proofs that this is true. Go look at the wiki article. Also, you can prove it by constructing the real numbers from axiomatic set theory. The point is, there is no counter proof, all you have is faulty reasoning. Also, do you except that geometric convergence in mathematics, for example 1/2+1/4+1/8+...=1. If so then you except that 0.999...=1. As all you need is r=1/10 and then have 9(1/10)+9(1/10)^2+....=1. Hence all you need to except is geometric convergence, which is accepted within mathematics. Calculus can use limits to reach as asymptotes There is something called analysis, seriously do you know any analysis? or how to prove stuff within analysis?

[drewmandan]

0.9 recurring is, by definition, a number that infinitely reaches towards 1 but never gets there. Actually, 0.9~ is by definition equal to 1 because of the axiom that every real number has two representations; in this case 1.0~ and 0.9~.

[juroara]

this forum needs a math section for all the nerds out there who think math is philosophy!

[Kushna Mufeed]

Math is to Philosphy as Binary is to Computer Programming.

[mini0991]

When I punch 0.9999999999 in on my TI-34 II, it returns 1 when equal is pressed. 0.9 repeated only appears to equal 1 because machines round it up.

[Kushna Mufeed]

That's a finite sequence of 9s. This is in the case of an infinite sequence.

[Abra]

This. Topic. Ismakingmecringe. Especially the logic about "it is really .999, but machines round up." The arguments I would bring in have already been noted (I thought I'd never "Thank" wendylove until today). Anyway, XKCD forum is planning on trolling the place tomorrow. Look what you've done.

[Kushna Mufeed]

I welcome them with open arms. ERTW

[drewmandan]

ERTW EAM (Engineers are morons).