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    1. #1
      When the ink runs out... Kushna Mufeed's Avatar
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      Does 0.9 repeated = 1?

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

      Quote Originally Posted by Jeff777 View Post
      I am not sorry or empathetic whatsoever for saying that I believe the world would be much better off without people like you in it. Have a great fucking day.
      [broken link removed]The Dynamics of Segrival[/URL]
      Discuss Segrival here
      See my other [broken link removed]

    2. #2
      FBI agent Ynot's Avatar
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      Quote Originally Posted by Kushna Mufeed View Post
      Are you going to try to tell me that something infinitely close to 1 isn't 1?
      yes

    3. #3
      Dream Squirrel Tamias.Squirrel's Avatar
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      Yes.

      EDIT: xD Ynot got to it first!
      ~Same squirrel, twice the carbs

      Area of focus: Dream Recall (Since October 6th, 2008)
      Current Goals: [x] Recall more than a fragment of a dream [ ] Recall more than one full dream in a single night
      Last Dream Recalled: Amigos!
      My Art Portfolio: Space Man Stuff (Short Poetry --> Phenomena --> Comedy)

    4. #4
      When the ink runs out... Kushna Mufeed's Avatar
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      Prove it

      Quote Originally Posted by Jeff777 View Post
      I am not sorry or empathetic whatsoever for saying that I believe the world would be much better off without people like you in it. Have a great fucking day.
      [broken link removed]The Dynamics of Segrival[/URL]
      Discuss Segrival here
      See my other [broken link removed]

    5. #5
      FBI agent Ynot's Avatar
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      Quote Originally Posted by Kushna Mufeed View Post
      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

    6. #6
      Wanderer Merlock's Avatar
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      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!

    7. #7
      FBI agent Ynot's Avatar
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      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

    8. #8
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      Quote Originally Posted by Ynot View Post
      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.

    9. #9
      Look away wendylove's Avatar
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      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.
      Last edited by wendylove; 10-23-2008 at 07:49 PM.
      Xaqaria
      The planet Earth exhibits all of these properties and therefore can be considered alive and its own single organism by the scientific definition.
      7. Reproduction: The ability to produce new organisms.
      does the planet Earth reproduce, well no unless you count the moon.

    10. #10
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      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.

    11. #11
      FBI agent Ynot's Avatar
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      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

    12. #12
      Look away wendylove's Avatar
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      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
      Xaqaria
      The planet Earth exhibits all of these properties and therefore can be considered alive and its own single organism by the scientific definition.
      7. Reproduction: The ability to produce new organisms.
      does the planet Earth reproduce, well no unless you count the moon.

    13. #13
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      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.
      Last edited by ninja9578; 10-23-2008 at 08:12 PM.

    14. #14
      Look away wendylove's Avatar
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      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.
      Last edited by wendylove; 10-23-2008 at 08:17 PM.
      Xaqaria
      The planet Earth exhibits all of these properties and therefore can be considered alive and its own single organism by the scientific definition.
      7. Reproduction: The ability to produce new organisms.
      does the planet Earth reproduce, well no unless you count the moon.

    15. #15
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      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.

    16. #16
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      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

    17. #17
      Look away wendylove's Avatar
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      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?
      Last edited by wendylove; 10-23-2008 at 09:02 PM.
      Xaqaria
      The planet Earth exhibits all of these properties and therefore can be considered alive and its own single organism by the scientific definition.
      7. Reproduction: The ability to produce new organisms.
      does the planet Earth reproduce, well no unless you count the moon.

    18. #18
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      Quote Originally Posted by Merlock View Post
      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~.

    19. #19
      Sleeping Dragon juroara's Avatar
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      this forum needs a math section for all the nerds out there who think math is philosophy!

    20. #20
      When the ink runs out... Kushna Mufeed's Avatar
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      Math is to Philosphy as Binary is to Computer Programming.

      Quote Originally Posted by Jeff777 View Post
      I am not sorry or empathetic whatsoever for saying that I believe the world would be much better off without people like you in it. Have a great fucking day.
      [broken link removed]The Dynamics of Segrival[/URL]
      Discuss Segrival here
      See my other [broken link removed]

    21. #21
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      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.

    22. #22
      When the ink runs out... Kushna Mufeed's Avatar
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      That's a finite sequence of 9s. This is in the case of an infinite sequence.

      Quote Originally Posted by Jeff777 View Post
      I am not sorry or empathetic whatsoever for saying that I believe the world would be much better off without people like you in it. Have a great fucking day.
      [broken link removed]The Dynamics of Segrival[/URL]
      Discuss Segrival here
      See my other [broken link removed]

    23. #23
      I am become fish pear Abra's Avatar
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      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.
      Abraxas

      Quote Originally Posted by OldSparta
      I murdered someone, there was bloody everywhere. On the walls, on my hands. The air smelled metallic, like iron. My mouth... tasted metallic, like iron. The floor was metallic, probably iron

    24. #24
      When the ink runs out... Kushna Mufeed's Avatar
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      I welcome them with open arms.

      ERTW

      Quote Originally Posted by Jeff777 View Post
      I am not sorry or empathetic whatsoever for saying that I believe the world would be much better off without people like you in it. Have a great fucking day.
      [broken link removed]The Dynamics of Segrival[/URL]
      Discuss Segrival here
      See my other [broken link removed]

    25. #25
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      Quote Originally Posted by Kushna Mufeed View Post

      ERTW
      EAM (Engineers are morons).

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