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

? about Godel's incomplete theorm

  1. Apr 11, 2006 #1
    I read the theorm and the proofs, but what i am unclear about is when is it used or what statments are unprovable. as far as i know it doesnt apply to Euclidean geometry so what branchs of math does it apply. part of the reason i am asking is on another website i seen someone try to use this theorm to show that .99... does not equal 1 and math itself is very flawed , i felt that the theorm is being misused but i probaly shouldf learn more before i say anything
     
  2. jcsd
  3. Apr 11, 2006 #2

    Zurtex

    User Avatar
    Science Advisor
    Homework Helper

  4. Apr 11, 2006 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    First, it is "incompleteness" theorem, not "incomplete" theorem. The theorem itself is complete. Essentially, it says that in any axiom system large enough to include the natural numbers is "incomplete"- that is that there exist statement which can neither be proven nor disproven. The proof of that theorem itself "constructs" a statement that can be proven nor disproven but in a very abstract way- it uses a way of assigning numbers to statements (the Godel numbering) such that the statement assigned a certain number be shown to neither provable nor disprovable- but doesn't tell us exactly what that number is and certainly not what the theorem is. Indeed, given a statement that cannot be proven nor disproven, we could take that statement (or its negation) as an axiom and have a new system- which would then have a new statement that could not be proved nor disproved.

    I can't imagine that having anything to do with 1= 0.999... That follows immediately from the definition of the base 10 numeration system.
     
  5. Apr 11, 2006 #4

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    As either Halls or Hurkyl is very keen to point out, the theory of Real Fields is complete and not remotely susceptible to this line of attack. Please post a link to this person's attempted disproof; I'm sure many people here would like to point out their egregious error.
     
  6. Apr 11, 2006 #5

    First off, godel's theorem talks about the existence of such a statement. It doesn't tell us what they are. Finding one/showing that a statement is undecidable is a lot harder. Examples: The Continuum hypothesis was shown to be undecidable within ZFC. I also know that the Goodstein's thoerem is an undecidable statement within peano arithmetic, however it can be proven with a stronger system. Whoever used godel's thm. to show that .999... does not equal 1 is 99.999999% probably a crackpot that has no idea what they are talking about.
     
    Last edited: Apr 11, 2006
  7. Apr 11, 2006 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I started to ask for a link but then it occured to me that I waste entirely too much time on that sort of thing already!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: ? about Godel's incomplete theorm
Loading...