Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A shorter proof to 0.999 = 1

  1. May 17, 2005 #1
    Here is Blizzard's proof that 0.999... = 1

    http://www.blizzard.com/press/040401.shtml


    My friend however, recently mentioned that:

    1/3 = 0.333...

    1.3 * 3 = 0.333... * 3

    1 = 0.999... also works.


    Has she discovered the shortest proof? Or is there something wrong here?
     
  2. jcsd
  3. May 17, 2005 #2
    This is perfectly right. I don't know if there's a "shortest proof", but your friend's certainly is short.

    I'm somehow a newbie here, but I used to visit Tom's Hardware Guide's forums, and there's an interesting topic with... various "opinions" on the subject on it. Check it out here
     
  4. May 18, 2005 #3
    There is, ofcourse,

    1/9 = 0.111....
    multiply be nine
    1 = 0.999.....
     
  5. May 18, 2005 #4

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I made a few contribution to that thread. SilverPig started that thread to see if the response was significantly different from a similar thread in the HiTech Forum at anantech, Which I also participated in.

    It was very disappointing that the majority of members of Anantech and Toms felt that it was not true.
     
  6. May 18, 2005 #5

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    That isn't a proof. Why is arithmetic deinfed on infinitely long decimals? In short, you're confusing real numbers with their representations as decimals. The fact that they are equal is immediate from the definition of the real numbers, not that anyone who thinks they're different even knows what the real numbers are.
     
  7. May 18, 2005 #6
    Matt - don't become worried - it isn't meant to be a proof - it is just a cunning trick used by high school mathematics teachers to trick their students and to make them think.

    No one is really saying that 0.9 recurring equals 1

    Regards

    Ben
     
  8. May 18, 2005 #7

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Oh great; the cranks come out of the wood work. Can we have an instant ban for anyone who, despite the explanation to the contrary being in the thread, asserts that they are not equal?

    Apologies if that's a typo and you clarifyting no one *denies* that they are equalivalent as representations of real numbers, or if | misunderstand and you are trying to differentiate between representations of real numbers and the numbers themselves, but I doubt that is your intention.
     
    Last edited: May 18, 2005
  9. May 18, 2005 #8

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I consider this sort of algebraic manipulation more of a demonstration then a proof. It is a valid demonstration of a mathematical fact, but not a proof.
     
  10. May 18, 2005 #9

    Zurtex

    User Avatar
    Science Advisor
    Homework Helper

    I'm saying 0.9 recurring equals 1 and so will any mathematical approch on it.
     
  11. May 18, 2005 #10

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Now, I don't know if I qualify as one of Zurtex' approch's (sounds like some lumbering, prehistoric animal to me), but I agree with his view as well.
     
  12. May 18, 2005 #11
    I think BENGOODCHILD was making the point that the value of 0.999... as a number is not 1.

    It is true that 0.999... comes from the formula for the series 9/10 + ;9/10^2 + 9/10^3,

    therefore the limit of the series is infact 0.999... and therefore one but the value is different.

    Unless we want to start the whole debate on infinity and what happens at the last 9 etc - well there i no last 9 becasue 0.99...is non-equatable. Okay?!


    -M
     
    Last edited: May 18, 2005
  13. May 18, 2005 #12

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Yes it it is, maverick (goodchild?). Learn about how real numbers are defined as equivalence classes on the set of (increasing, bounded) sequences of rationals.
     
    Last edited: May 18, 2005
  14. May 18, 2005 #13

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Who would have to talk about infinity and the last 9? You, Maverick? Only those who don't understand mathematics would cite that. Indeed there is no reason to invoke infinity at all, indeed the appearance of any infinty is only a short hand fomr something to do with finite things and we need not ever mention it. Now, as I'm apparently not in a charitable mood, can the cranks go away?

    All refutations of this fact arise from not understanding maths - the definitions are straight forward, though hard to visualize perhaps, but in the completion of Q (ie R) those are the same number. Fin. Just as 1/2 and 2/4 are the same rational number.
     
  15. May 18, 2005 #14

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I think BenGoodchild was making a joke.

    I hope maverickmathematics was also (look at the user name!).
     
  16. May 18, 2005 #15
    we're studying at Trinity College Cambridge- look at the notes mav posted about number theory, so yes I'm messing you guys around.

    and maverick is a long time friend of mine so there you go

    regards,

    Ben
     
    Last edited by a moderator: May 18, 2005
  17. May 18, 2005 #16

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Level of jocular funniness:
    Harrumph, heh-heh
     
  18. May 18, 2005 #17

    matt grime

    User Avatar
    Science Advisor
    Homework Helper


    I note you've added things since your orignal post.

    Funny? Nurse, my sides have split.
     
  19. May 18, 2005 #18
    you guys are just plain boring - you'll get all worked up if I tell you that 2+2=5 and start crying...
     
  20. May 18, 2005 #19

    Zurtex

    User Avatar
    Science Advisor
    Homework Helper

    I'm studying number theory at UMIST and I'm sure half the people in my class wouldn't know that 0.999... = 1 :grumpy:
     
  21. May 18, 2005 #20

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    And, from BenGoodchild's second post, I don't think he knows either.
    This damage control action he's undertaken afterwards is unconvincing.
     
    Last edited: May 18, 2005
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: A shorter proof to 0.999 = 1
  1. 1=0.999 again (Replies: 17)

  2. 0.999 = 1 (Why?) (Replies: 5)

  3. More 0.999~ vs 1 (Replies: 60)

  4. 0.999 = 1 ? (Replies: 2)

  5. 0.999 = 1 (Replies: 6)

Loading...