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.