Date: Mar 23, 2013 2:08 PM
Author: Mike Terry
Subject: Re: Matheology � 224
"David R Tribble" <david@tribble.com> wrote in message

news:85d0c23d-7dcd-4607-b22d-d2444df80433@googlegroups.com...

> WM wrote:

> >>... consider the list of finite initial segments of natural numbers

> > 1

> > 1, 2

> > 1, 2, 3

> > ...

> >

> > According to set theory it contains all aleph_0 natural numbers in its

> > lines. But is does not contain a line containing all natural numbers.

> > Therefore it must be claimed that more than one line is required to

> > contain all natural numbers. This means at least two line are

> > necessary.

>

> That is correct. In fact, all Aleph_0 lines are required

> (necessary sufficient) to contain all of the naturals.

This is sufficient but not necessary. (Aleph_0 lines are necessary and

sufficient.)

Mike.