```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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