Date: Jan 22, 2013 3:57 PM
Author: Virgil
Subject: Re: ZFC and God

In article 
<575ebd3c-c814-472b-839f-65db2baf79e0@f19g2000vbv.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> A) $\mathbb{N} = \bigcup_{n=1}^\infty$ {n}
> and also the union of all FISONs yields
> B) $\mathbb{N} = \bigcup_{n=1}^\infty$ {1, 2, ..., n}
> because it cannot be less than A.
> Do you agree that the actually infinite path {1, 2, ...} does not
> differ from B, such that "behind" every natural nothing can happen? In
> particular the inclusion of {1, 2, ...} does not change anything in B?
> Therefore {1, 2, ...} cannot differ from the union B?
>
> By the way, every FISON, which stands for finite initial segment of
> the naturals, is finite. This does not change by unioning as many as
> are available. The union never gets larger than every FISON. Can you
> understand that?
>
> Regards, WM


In standard set theory, every FISON is a proper subset of another FISON,
So there is maximal FISON, and the union of all of them cannot itself be
a FISON, since that would require it to be a proper subset of a subset
of itslf.

Given the family of sets F = {{1}, {1,2}, {1,2,3}, ...}, WM would have
us believe that F is a member of F, which may be allowed in WMYTHEOLOGY
but is not allowed in ZFC or any common set theory.
--