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 B
There 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 it
WM 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 > behaviour
Then WM should learn to be responsible for his behavior. --
