Date: Mar 24, 2013 3:39 PM
Author: Virgil
Subject: Re: Matheology � 224
In article

<faa9a94f-236e-4066-8cd4-12f33f8a8df3@m12g2000yqp.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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

A red letter day, WM is finally RIGHT about something!

But if David had left out the world "all", and said merely

"In fact, Aleph_0 lines are required

(necessary sufficient) to contain all of the naturals."

then David would have been correct, since EVERY set of aleph_0 lines is

sufficient but no set of less than aleph_0 lines is sufficient.

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