```Date: Feb 5, 2013 5:37 PM
Author: Virgil
Subject: Re: Matheology � 203

In article <3c52bc20-0b3f-4074-8307-387942aef034@z9g2000vbx.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 5 Feb., 12:17, William Hughes <wpihug...@gmail.com> wrote:> > On Feb 5, 10:38 am, WM <mueck...@rz.fh-augsburg.de> wrote:> > <snip>> >> > > So "there is no list of X" is> > > true for every potentially infinite set.> >> > And so it goes.  Now there is no list> > of |N.> > Now? Why should there ever have been a complete list, that means a> complete sequence, that means all terms with all their indices which> are all natural numbers which do not exist?If not all natural numbers exist then some of them must not exist.WHich ones?> >> > So ends this round.  It has> > taken 100 posts to get WM to> > admit that different potentially> > infinite sets have different> > listability.> > Where had I conceded the complete existence of a list?Unless every set is listable, there must be sets which are not listable,so which is it in WMytheology? Is every set listable or are some sets not listable?> > > It would take another> > 100 posts to get him to admit> > that he admitted it.> >> > We now know> > that the potentially infinite> > series 0.111...> >> > is not a single line of the list> >> > 0.1000...> > 0.11000...> > 0.111000...> > ...> > And we know When WM says "we know" something, it does not mean that anyone other than WM "knows" it.> >> > More importantly, we have learned that> > we can use induction to show "every"> > and that "every n -> P(n)" is equivalent> > to "there is no m such that ~P(m)"> > So we do not need to resort to "all"> > to show something does not exist.> > Of course, that is true. For instance we can show that no list exists,> that contains, as indices, all natural numbers.Then let u see you try to show it without appealing to any of those "axioms" that only hold in WMytheology and not elsewhere.And if your believe you have a better set theory than, say, ZF, produce an axiom system for it of equal clarity to the one for ZF.Note that, in ZF, if A is a set then the union of {A} with A is also a set, but apparently this rule does not hold in any set theory in WMytheology.--
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