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