Re: The RM, Newtonian mechanics, algrebra and incompleteness
From: Torkel Franzen <torkel_at_sm.luth.se>
Date: 04 Jun 2004 10:38:48 +0200
Message-ID: <vcbvfi7ra3r.fsf_at_beta19.sm.ltu.se>
Date: 04 Jun 2004 10:38:48 +0200
Message-ID: <vcbvfi7ra3r.fsf_at_beta19.sm.ltu.se>
"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 - 10:38:48 CEST