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.

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