Date: Jan 30, 2013 5:33 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God
On 30 Jan., 09:47, Virgil <vir...@ligriv.com> wrote:

> In article

> <4a768b6d-0d71-4e89-bf77-6b70d6e5e...@d11g2000yqe.googlegroups.com>,

>

>

>

>

>

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

> > 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

>

> You just gave it one.

>

No. I know, it is very unfamiliar, but it is fact: "0.111..." is not a

decimal expansion. For instance, because decimal expansions by

definition have only one point. 0.111... is a finite definition of 1/9

like 1/9 is itself. It formulates a task, namely to find the n-th

digit of the decimal expansion. This task can be accomplished for

every n, but not for all.

Regards, WM