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
