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