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, WMIn 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.--