Date: Feb 5, 2013 11:36 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: WMytheology § 203

On 5 Feb., 16:53, fom <fomJ...@nyms.net> wrote:
> On 2/5/2013 4:11 AM, WM wrote:
>

> > On 5 Feb., 01:26, Virgil <vir...@ligriv.com> wrote:
>
> >> If, as WM claims, there are at most countably many ways of accessing
> >> reals and, as Cantor claimed, there are more than countably many reals,
> >> then ...

>
> > Then the axiom that every real can be put in trichotomy with every
> > rational number is contricted. Then ZFC contradicts analysis.

>
> In the logical type hierarchy that *defines* a real number,
> the order relation of the rationals is inherited.  The
> rationals that are reals are distinct from the rationals
> from which the real numbers are defined.


Please name a difference that can be proved to exist in mathematics.
Same is untrue for naturals and positive finite cardinals. There is
not the least difference with respect to mathematics.

>  In this construction,
> the identity of a real number is tied to the trichotomy of
> the underlying rationals and to the fact that in the complete
> space any given pair of irrationals taken to be distinct are
> linearly separated by a rational.


That fact already proves that there cannot exist more irrationals than
rationals.
>
> The problem of identity of a real number as part of the
> real number system relative to identity within
> Zermelo-Fraenkel set theory is a pseudo-metrization
> problem.


No, it is the clever trick of selling matheological nonsense as ideas
of intelligent heads to innocent believers in the existence of
intelligent mathematicians.

Regards, WM