MoeBlee
Posts:
1,277
Registered:
5/9/11
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Re: Eliminating Quantifiers For Dummies! A(x) E(y) ALL(t)EXIST(u)EaAb ..
Posted:
Jan 11, 2012 4:54 PM
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On Jan 11, 3:43 pm, Dan Christensen <d...@dcproof.com> wrote:
> On Jan 11, 3:26 pm, Jack Campin <bo...@purr.demon.co.uk> wrote:
>
> > > Just to be clear, do you see the axioms of first-order group theory
> > > (Mendelson's 7 axioms with their explicitly unbounded quantifiers)
> > > to be a workable, alternative set of axioms for that branch of
> > > mathematics we call group theory, or not.
>
> > Just to be clear, do you see the axioms of Peano arithmetic to be a
> > workable, alternative set of axioms for that branch of mathematics
> > we call real analysis, or not?
>
> Haven't you heard? The real numbers can be constructed from the set of
> natural numbers.
But that is ordinarily done not in PA but rather in set theory.
MoeBlee
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