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