Date: Mar 24, 2013 10:30 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<392bc935-a976-4823-9bec-81edea972e6d@k8g2000yqb.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 24 Mrz., 20:29, fom <fomJ...@nyms.net> wrote:
> > On 3/24/2013 10:13 AM, William Hughes wrote:
> >
> >
> >
> >
> >

> > > On Mar 24, 4:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > >   Induction proves that every
> >
> > > True
> >
> > >   and all
> >
> > > False
> >
> > >> finite lines
> > >> of our list can be removed without changing the contents,

> >
> > Nice!

>
> Yes, I agree. Here he shows that FOPL of ZFC is not what he wishes to
> be applied.


Wrong! What he has shown is that one must stay outside Wolkenmuekenheim
to do any actual mathematics.

An ISON is an non-empty Initial Set Of Naturals, so must contain all
the naturals preceding any each of its members.

A FISON is a Finite ISON.

The union of any set of ISONs is an ISON.

For the 1-origin naturals, the first few FISONs are
{1}, {1,2}, {1,2,3}, {1,2,3,4}, and so on.

The corresponding set of all naturals is indicated by |N , or
{1,2,3,...}.

The union of any non-empty set of FISONS is either a FISON or the
unique non-finite ISON denoted by |N.

For finite such non-empty sets it is always the largest by inclusion
FISON in the set, and for any other non-empty set of FISONs it is
always |N.
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