[math-fun] Fermat's Last Theorem question
Peano's axioms suffice to define the integers, and hence (?) real & complex numbers, eh? And you are claiming you'd be "surprised" if Fermat's Last Thm was proven using those alone?!?! I'm freaking surprised if more is needed. In fact, I'm shaken. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
Who are you referring to, Warren? --Dan On 2013-02-21, at 8:37 PM, Warren Smith wrote:
Peano's axioms suffice to define the integers, and hence (?) real & complex numbers, eh? And you are claiming you'd be "surprised" if Fermat's Last Thm was proven using those alone?!?! I'm freaking surprised if more is needed. In fact, I'm shaken.
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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On Thu, Feb 21, 2013 at 11:41 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Who are you referring to, Warren?
--Dan
On 2013-02-21, at 8:37 PM, Warren Smith wrote:
Peano's axioms suffice to define the integers, and hence (?) real & complex numbers, eh?
I don't see how you can define the reals from the Peano axioms. They let you talk about individual integers, and you can therefore translate statements about the rationals into statements about pairs of integers, but statements about the reals are statements about sets of integers or infinite sequences of integers, and you can't talk about those in Peano arithmetic.
And you are claiming you'd be "surprised" if Fermat's Last Thm was proven using those alone?!?! I'm freaking surprised if more is needed. In fact, I'm shaken.
The proof of FLT is in ZFC, or nearly so; at worst, in ZFC + Consis(ZF).. But I doubt it can be formalized in Peano arithmetic. Andy
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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-- Andy.Latto@pobox.com
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Andy Latto -
Dan Asimov -
Warren Smith