Date: Feb 22, 2013 4:43 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

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.

Regards, WM