? about Godel's incomplete theorm

[raven1]

I read the theorm and the proofs, but what i am unclear about is when is it used or what statements are unprovable. as far as i know it doesn't 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 probably shouldf learn more before i say anything

 

[Zurtex]

Pretty good explanation here: http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorem

 

[HallsofIvy]

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.

 

[matt grime]

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.

 

[gravenewworld]

I read the theorm and the proofs, but what i am unclear about is when is it used or what statements are unprovable. as far as i know it doesn't 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 probably shouldf learn more before i say anything

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.

 

[HallsofIvy]

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.

I started to ask for a link but then it occurred to me that I waste entirely too much time on that sort of thing already!