```Date: Feb 23, 2013 4:15 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <62781b70-dff9-4093-85d0-ff6e5bfcbbb8@u20g2000yqj.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 22 Feb., 23:39, Virgil <vir...@ligriv.com> wrote:> > In article> > <6cfcca98-d4e5-475d-a4bf-168639050...@n2g2000yqg.googlegroups.com>,> >> >> >> >> >> >  WM <mueck...@rz.fh-augsburg.de> wrote:> > > On 22 Feb., 22:29, Virgil <vir...@ligriv.com> wrote:> > > > In article> > > > <c3c197e4-2161-4ecf-a84e-d479adb05...@k4g2000yqn.googlegroups.com>,> >> > > >  WM <mueck...@rz.fh-augsburg.de> wrote:> > > > > On 21 Feb., 21:51, Virgil <vir...@ligriv.com> wrote:> >> > > > > > > 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.> >> > > > > By definition of A we know it is never empty.> >> > > > There is no such thing as an "A" but only an infinite sequence of> > > > differing A's, indexable by the infinite set of natural numbers,> >> > > In any case there is never an A = { }.> > > Therefore similarly there is never a B = |N.> >> > There is never an A or a B which is a subset of |N either, though their> > members are subsets of |N.> > You are in error.> The set A_1 = {1} is a subset of |N.But A_1 is merely a member of the sequence A, and is not A itself.> The set B_1 = { } is a subset of |NBut B_1 is merely a term of sequence B and not equal to B.SO it is WM who is in error by trying to make A stand for two different things at once, and  B stand for two different things at once.WM's A and B can only stand for the whole of a sequence or for one term in that sequence  but not for both simultaneously, as he is trying to make them do.--
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