```Date: Feb 23, 2013 4:43 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 23 Feb., 22:15, Virgil <vir...@ligriv.com> wrote:> In article> <62781b70-dff9-4093-85d0-ff6e5bfcb...@u20g2000yqj.googlegroups.com>,>>>>>>  WM <mueck...@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.A_1 is A in the first step.>> > The set B_1 = { } is a subset of |N>> But B_1 is merely a term of sequence B and not equal to B.B_1 is B in the first setp.Regards, WM
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