Date: Feb 22, 2013 4:29 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<c3c197e4-2161-4ecf-a84e-d479adb05882@k4g2000yqn.googlegroups.com>,
WM <mueckenh@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,

> That implies that B

There is no such thing as a "B" but only an infinite sequence of
differing "B's, indexable by the infinite set of natural numbers.
,
> never contains all natural numbers. B always has a last element

B is an infinite sequence of subset of N, thus does not have any "last
elements, even though each member of B may have a last member.

> but
> we cannot know it



WM cannot know lots of things because he has put a lock on his brain
that prevents it.


> That is the property of infinity. I am not responsible for that
> behaviour


Then WM should learn to be responsible for his behavior.
--