Date: Jan 25, 2013 5:07 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God
On 25 Jan., 19:58, Virgil <vir...@ligriv.com> wrote:

> In article

> <23c75ce4-2ede-43e1-87d2-a61866fe1...@w3g2000yqj.googlegroups.com>,

>

>

>

>

>

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

> > On 25 Jan., 01:23, Virgil <vir...@ligriv.com> wrote:

> > > In article

> > > <1bff3260-2afe-4cb5-b296-cbfcd9313...@x3g2000yqo.googlegroups.com>,

>

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

> > > > On 24 Jan., 21:43, Virgil <vir...@ligriv.com> wrote:

>

> > > > > > > U_n {1,...,n} is not infinite. (*)

>

> > > > > > It is not actually infinite. The cardinality is not larger than every

> > > > > > n.

>

> > > > > Then there must be some n that it is not larger than.

>

> > > > > Either

>

> > > > There can be every n. Because no n is infinite!

>

> > > If there can be "every n", then there can be set containing "every n".

>

> > There can be the set of all terminating decimal fractions (0. d_1,

> > d_2, ..., d_n), containing every n as the last digit, is a set without

> > non-terminating decimal fraction, isn't it?

>

> How would the existence of such a set prevent the existence of a set of

> all decimals between 0 and 1?

That is not our question and not our problem. We work within the

proposed restriction until we discover a digit (i.e., an index of a

digit) that is not in an element of the set of all terminating decimal

representations of all real numbers of the unit interval and forces us

to extend the domain.

Regards, WM