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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