Date: Feb 5, 2013 11:36 AM
Subject: Re: WMytheology § 203

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

> > On 5 Feb., 01:26, Virgil <> 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
> 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