Date: Mar 24, 2013 7:48 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 23 Mrz., 18:48, David R Tribble <da...@tribble.com> wrote:

> 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.

That claim is easily disproved.

For all n in N: The first n lines are neither necessary nor sufficient

to contain all of the naturals.

.

Regards, WM