In article <e7e81426-39b7-4717-a883-61dfce10344a@9g2000yqy.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 23 Feb., 22:15, Virgil <vir...@ligriv.com> wrote: > > In article > > <62781b70-dff9-4093-85d0-ff6e5bfcb...@u20g2000yqj.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 22 Feb., 23:39, Virgil <vir...@ligriv.com> wrote: > > > > In article > > > > <6cfcca98-d4e5-475d-a4bf-168639050...@n2g2000yqg.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 22 Feb., 22:29, Virgil <vir...@ligriv.com> wrote: > > > > > > In article > > > > > > <c3c197e4-2161-4ecf-a84e-d479adb05...@k4g2000yqn.googlegroups.com>, > > > > > > > > WM <mueck...@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, > > > > > > > In any case there is never an A = { }. > > > > > Therefore similarly there is never a B = |N. > > > > > > There is never an A or a B which is a subset of |N either, though their > > > > members are subsets of |N. > > > > > You are in error. > > > The set A_1 = {1} is a subset of |N. > > > > But A_1 is merely a member of the sequence A, and is not A itself. > > A_1 is A in the first step.
Outside of WMytheology, that is not how things work.
Things like A and B, are either entire sequences of sets or not sequences of sets, and if sequences, only their indexed members can be specific sets of such sequences. > > > > > The set B_1 = { } is a subset of |N > > > > But B_1 is merely a term of sequence B and not equal to B. > > B_1 is B in the first setp.
Outside of WMytheology, that is not how things work. --
