```Date: Feb 21, 2013 3:51 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <2bf7c594-8e66-4624-94d3-b1e05946811f@9g2000yqy.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 20 Feb., 23:27, William Hughes <wpihug...@gmail.com> wrote:> > >> > > > For every natural number n we have> > > >     the nth line of L and x> > > >     are not coFIS> >> > > > true?-> >> > > True> >> > Is the statement> >> > There is no natural number m> > such that the mth line of L and x> > are coFIS> >> > true?-> > No, the statement is wrong. The true statement is: We cannot find the> largest number such that the mth line and x are coFIS. Again you> assume actual infinity for x.> > Consider the union of ordered sets in ZF:> (1, )> (1, 2, )> (1, 2, 3,  )While I am aware of sets in ZF standardly used to represent 1,2,3, and so on, and even 0, I am not aware of any set in ZF that represents a blank. And everything in ZF is a set, so without such a set there cannot be a blank in ZF.> > Each set has a blank.Not in ZF. WM goofs as usual!> > Or consider the union of natural numbers in a set B while there> remains always one number in the intermediate reservoir A.> >      A              B> --> 1         -->{ }> --> 2,1      -->{ }> --> 2         -->1> --> 3, 2     -->1> --> 3         -->1, 2> --> 4, 3     -->1, 2> --> 4         -->1, 2, 3> ...> --> n         -->1, 2, 3, ..., n-1> --> n+1, n -->1, 2, 3, ..., n-1> --> n+1     -->1, 2, 3, ..., n-1, n> ...> > One would think that never all naturals can be collected in B, since a> number n can leave A not before n+1 has arrived.> > Of course this shows that ZF with its set of all natural numbers is> contradicted.WM's A and B are not sets but sequences of sets, so if WM wants to consider a limit to any such sequences, he must first define what he means by such a limit, as there is no universal definition for "the" limit of a sequence of sets.> Presumably it is this recognition that raises your> interest in potential infinity of analysis.WM's presumptions are again wrong.> Therefore the set> 0> 10> 110> 1110> ...> has a line that is coFIS with 111... (up to every n - and more is not> feasible).Only in WMytheology. Everywhere else a line containing 0 can never be coFIS with a line not containing 0.--
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