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. > > One could certainly construct a system of definitions > wherein they would be defined differently
"standard mathematics" would be an example for the initiate.
>-- in > one case the range of a function from some ordinal > sequence and in the other a nesting of ordered pairs. > But, without a formal system of definitions to make > some sort of distinction, they mean the same. > > So, S is a sequence of sequences.