Date: Mar 24, 2013 3:31 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<f91c46a2-26b2-4ba5-90f4-7b6476787bbf@f5g2000yqp.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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.



Any set of Aleph_0 lines are required but not all lines are required!

> > 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.


WM has no valid proofs outside Wolkenmuekenheim

The only sets of lines of cardinality LESS THAN aleph_0 are finite sets
of lines, and no finite set of lines contains any more naturals that its
finite last line contains.

So that WM is WRONG! AGAIN!! AS USUAL!!!
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