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.

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