Date: Jan 25, 2013 5:13 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God

On 25 Jan., 20:18, Virgil <vir...@ligriv.com> wrote:
> In article
> <b443b0b0-2e03-4179-ab2f-dec89805d...@u16g2000yqb.googlegroups.com>,
>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 25 Jan., 09:47, Virgil <vir...@ligriv.com> wrote:
>
> > > > > > Then ponder a while about the following sequence
>
> > > > > > d
>
> > > > > > d1
> > > > > > 2d

>
> > > > > > d11
> > > > > > 2d2
> > > > > > 33d

>
> > > > > > and so on. In every square there are as many d's as lines. The same
> > > > > > could be shown for the columns.

>
> > > > > Yes, in this sequence of three squares, what you say is true.
>
> > > > Is there a first square where my observation would fail?
>
> > > Since you claim every line is necessarily finite, but the number of
> > > lines is not, there will be a number of lines greater than the number of
> > > digits in your finite first line.

>
> > In an ordered set like the sequence of squares above, we have for
> > every subset a first element. If you claim to know a square that is
> > not a square, then there must be a first square that is not a square.

>
> If n is the number of digits in the first entry to your list, then you
> have no more than n such squares as that first entry will be too short
> for any more.


If there follows an entry with more digits, the preceding entries can
be extended by zeors without leaving the domain of terminating
decimals.

Regards, WM