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.