Date: Mar 25, 2013 5:19 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<15b5fdfe-65c7-439f-9491-60ad1bafddde@p5g2000yqj.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 24 Mrz., 22:35, Virgil <vir...@ligriv.com> wrote:
>

> >
> > The theorem does not cover what will transpire when two or more
> > lines, along with all their predecessors, are removed.

>
> There is no reason to remove more than one line with all its
> predecessors, because it can be proved that all lines are
> predecessors of a line, since there is no line without follower.

> >
> > So it is of some interest to note that for any set of lines having
> > a maximal line in it, what WM claims (that one can remove any line
> > frm any set of lines without affecting the union of the set of lines)
> > is false. At least everywhere outside Wolkenmuekenheim


>
> Does induction not hold for the infinite set of naturals?


Not in Wolkenmuekenheim.

>
> > > >
> > > >
> > > >

>
> >
> > > > However, we do not know what will happen if we remove an
> > > > infinite number of finite lines.

> >
> > > That's why we use induction.
> >
> > Except that no inductive argument will go from removing a finite
> > set of lines to removing an infinite set of lines,

>
> Induction holds


It does not hold that removing the largest member of a set having a
unique largest member reproduces the original set exactly.

At least it does not do so outside of Wolkenmuekenheim, even though WM
claims ti does so everywhere.
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