```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 theway-back machine may not have a halt
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