Date: Feb 23, 2013 6:37 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<e7e81426-39b7-4717-a883-61dfce10344a@9g2000yqy.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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.


Outside of WMytheology, that is not how things work.


Things like A and B, are either entire sequences of sets or not
sequences of sets, and if sequences, only their indexed members can be
specific sets of such sequences.
> >
> > > 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.


Outside of WMytheology, that is not how things work.
--