```Date: Feb 22, 2013 6:12 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

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 Bnever contains all natural numbers. B always has a last element, butwe 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 thatbehaviour, I only recall what our ancestors knew.Regards, WM
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