• • # Thread: Does 0.9 repeated = 1?

1. ## Does 0.9 repeated = 1?

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

2. Originally Posted by Kushna Mufeed Are you going to try to tell me that something infinitely close to 1 isn't 1? yes  Reply With Quote

3.  Yes. EDIT: xD Ynot got to it first!  Reply With Quote

4.  Prove it  Reply With Quote

5. Originally Posted by Kushna Mufeed 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  Reply With Quote

6.  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!  Reply With Quote

7.  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  Reply With Quote

8. Originally Posted by 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 I was going to say something like that.  Reply With Quote

9.  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.  Reply With Quote

10.  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.  Reply With Quote

11.  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  Reply With Quote

12.  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  Reply With Quote

13.  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.  Reply With Quote

14.  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.  Reply With Quote

15.  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.  Reply With Quote

16.  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  Reply With Quote

17.  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?  Reply With Quote

18. Originally Posted by Merlock 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~.  Reply With Quote

19.  this forum needs a math section for all the nerds out there who think math is philosophy!  Reply With Quote

20.  Math is to Philosphy as Binary is to Computer Programming.  Reply With Quote

21.  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.  Reply With Quote

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

23.  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.  Reply With Quote

24.  I welcome them with open arms. ERTW  Reply With Quote

25. Originally Posted by Kushna Mufeed ERTW EAM (Engineers are morons).  Reply With Quote

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