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