Date: Mar 25, 2013 8:07 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 25 Mrz., 00:49, Virgil <vir...@ligriv.com> wrote:

> In article

> <39dd320b-1f56-4cf7-bb03-f0f634420...@l5g2000yqe.googlegroups.com>,

>

> WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 24 Mrz., 20:39, Virgil <vir...@ligriv.com> wrote:

>

> > > But if David had left out the world "all", and said merely

> > > "In fact, Aleph_0 lines are required

> > > (necessary sufficient) to contain all of the naturals."

> > > then David would have been correct, since EVERY set of aleph_0 lines is

> > > sufficient but no set of less than aleph_0 lines is sufficient.

>

> > We know your statements of faith. But where do you get aleph_0 lines

> > without using lines of the infinite set of aleph_0 lines that, as

> > provable in mathematics, are not sufficient?

>

> Which infinite sets of lines does WM claim are provably not sufficient?

All FISONs are not sufficient, because forall F in the set of FISONs:

There are infinitely many natural numbers not covered by F and all its

predecessors and all its followers.

> THEOREM: To have a subset of the infinite set of lines(FISONs) whose

> union is |N, it is both necessary and sufficient that that subset of

> lines also be infinite.

Nonsense. All FISONs cannot be sufficient, since no FISON is

necessary.

Corollary: To catch a unicorn it is both necessary and sufficient to

ask an infinity of horses to help.

>

> This theorem is valid

and its corollary is suitable, to show the strenght of ZFC.

Regards, WM