Date: Mar 24, 2013 7:50 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 23 Mrz., 19:08, "Mike Terry"

<news.dead.person.sto...@darjeeling.plus.com> wrote:

> "David R Tribble" <da...@tribble.com> wrote in messagenews: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.)

>

This is a false claim, if induction is valid and if |N has more

elements than every finite line.

For aleph_0 lines, namely every finite line, my proof shows that they

are not necessary.

Regards, WM