```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 BThere 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 itWM 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> behaviourThen WM should learn to be responsible for his behavior.--
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