Date: Feb 22, 2013 8:09 AM
Author: fom
Subject: Re: Matheology § 222 Back to the root<br> s

On 2/22/2013 5:12 AM, WM 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. That implies that B
> never contains all natural numbers. B always has a last element, but
> we cannot know it, because if we say n, then n+1 is as well in B.
>
> That is the property of infinity. I am not responsible for that
> behaviour, I only recall what our ancestors knew.
>
> Regards, WM
>


We have determined that it is time prior to Pythagoras.

If there are no natural numbers greater than 60 the
way-back machine may not have a halt