Date: Jan 30, 2013 3:07 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God
On 30 Jan., 02:17, Virgil <vir...@ligriv.com> wrote:

> In article

> <6a9608a5-ec9c-4e81-af59-ae4caa19b...@h2g2000yqa.googlegroups.com>,

>

> WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 28 Jan., 22:52, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

> > > Now,

> > > if every real has a terminating decimal representation, then...

>

> > I did not say that every real has a terminating representation.

>

> But does every real accessible real have a decimal expansion, at least

> in theory?

No.

>

> Does every rational have a decimal expansion?

No. For instance 1/9 = 0.111... has no decimal expansion but only

approximations. The limit of the increasing and converging sequence

0.1, 0.11, 0.111, ... cannot be expressed by a decimal expansion.

Every attempt to produce aleph_0 digits has yet failed at a finite

index. There may be infinitely many attempts. And beyond is nothing

but matheology.

If you believe in the existence of a decimal expansion of 1/9 in some

matheological heaven, why not write it here on earth?

Regards, WM