Re: The RM, Newtonian mechanics, algrebra and incompleteness

"mountain man" <hobbit_at_southern_seaweed.com.op> writes:

> I think you should double-check the above. Godel's incompleteness
> theorem was a statement in elementary number theory (arithmetic).

  Statements of arithmetic cannot be expressed in the language of the theory of the real field. This is because although the natural numbers are a subset of the real numbers, you cannot define "(the real number) x is a natural number" using only +,*,0,1,= and quantification over the real numbers. Received on Fri Jun 04 2004 - 03:38:48 CDT