Date: Mar 23, 2013 1:48 PM
Author: David R Tribble
Subject: Re: Matheology § 224

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.