On 2007.07.09 11:47:42, you,
the extraordinary Jose Mario Quintana, emitted:
<...>
>
> To complicate matters, at least for me, there is a result by Tarski implying
> that (an axiomatic version of) the field of real numbers is complete. I am
> not familiar with its proof and I do not know how to reconcile it with the
> former statement [that elementary number theory is incomplete].
<...>
Back in the day, some suggested that this might
seem less surprising if one considered Fermat's
"theorem":
There is no N > 2 such that x^N + y^N = z^N
x,y,z ranging over the integers >1. If there were a
complete proof procedure for elementary number
theory this would be easy to show true or false
("in principle" :-). For x,y,z ranging over real
numbers, it's obvious the "theorem" is false.
--
Nollaig MacKenzie
http://www.amhuinnsuidhe.net
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