In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 20 Apr., 18:36, fom <fomJ...@nyms.net> wrote: > > On 4/20/2013 11:20 AM, WM wrote: > > > > > On 20 Apr., 17:18, fom <fomJ...@nyms.net> wrote: > > >> On 4/20/2013 3:16 AM, WM wrote: > > > > >>> Matheology § 255 > > > > >>> 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?. > > > > Ordered set and sequence generally mean the same thing. > > Why then do you say "not sets"? But you are wrong. Sets contain an > element only once, while a sequence like 1, 1, 1, ... can contain it > more than once.
Thus while a suitably well-ordered set is always a sequence, a sequence need not be an ordered set? But there is considerable overlap. > > > > One could certainly construct a system of definitions > > wherein they would be defined differently > > "standard mathematics" would be an example for the initiate.
But WM rejects far too much of standard mathematics in favor of his own WMytheology to rely on standard mathematics to convince WM about anything. --