In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 20 Apr., 17:18, fom <fomJ...@nyms.net> wrote: > > On 4/20/2013 3:16 AM, WM wrote: > > WMytheology Sucks > > > > > Let S = (1), (1, 2), (1, 2, 3), ... be a sequence of all finite > > > initial sets s_n = (1, 2, 3, ..., n) of natural numbers n. > > > > Not sets. > > > > Sequences. > > In contrast to curly brackets parentheses indicate ordered sets. Here > we have a sequence of ordered sets which is a sequence of sets, isn't > it?. > > > > > > > > > Every natural number is in some term of S. > > > U s_n = |N > > > > Notice the use of a union here. > > > > What is the index of the union. > > 1 to oo
Better is to use the ZF definition of union in which the union of a set of sets is the set of all members of those members of that set.
Then Union(S)= |N.
> > > > Union_i (i e |N) s_i > > > > In other words, this is disallowed in WM's > > world
But the ZF union cannot be disallowed by WM, since WM himself "created" the set S, so must allow it. --