Re: Han's startling new set theory.

Timothy Little wrote:
> cbrown@xxxxxxxxxxxxxxxxx wrote:
> > So you believe that it "might be possible" that there are co-prime
> > natural numbers p and q, such that p^2 = 2*q^2?
>
> It depends what you mean by "natural numbers", co-prime and so forth.
> Usually these terms are defined in terms of some particular system,
> and these systems aren't necessarily all equivalent.
>
> For example, I'm not certain that we can't derive a suitably
> formalized version of "there exists p,q in N such that p^2 = 2 q^2"
> from the axioms of, say, ZFC.
>
> I'm more confident (very very confident, but still not absolutely
> certain) that we can't derive such a theorem from PA.
>

Let's work in the axioms of PA. Suppose we take a more constructivist
approach, and demand instead that an existence proof alone is
insufficient; you must present me with a construction for naturals p
and q such that 2*q^2 = p^2.

How is it not "certain" in your mind that this is not possible?

Cheers - Chas

.

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