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.
One could certainly construct a system of definitions wherein they would be defined differently -- 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.