Re: [math-fun] math, existence, and God
No, they weren't. If FLT had turned out to be false, it would have been provably false, by just doing the arithmetic for a counterexample. --Dan << Quoting Dan Asimov <dasimov@earthlink.net>:
I am assured by logicians that in any axiomatic system rich enough to include number theory, there are propositions that can be neither proved nor disproved, regardless of whether they are "really" true or "really" false.
A common example that may be of this type is the twin primes conjecture (TWP).
Not so long ago, people were saying this about Fermat's Last Theorem.
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
On Tue, Jul 14, 2009 at 5:35 PM, Dan Asimov <dasimov@earthlink.net> wrote:
No, they weren't.
If FLT had turned out to be false, it would have been provably false, by just doing the arithmetic for a counterexample.
But it was (until Wiles' proof, of course) possible that FTL was impossible to prove. It's just that if it were impossible to prove, it would also be impossible to prove that it was impossible to prove, since a proof that it was impossible to prove would constitute a proof that it was true, from your logic above. Andy
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Dan Asimov