In article <email@example.com>, firstname.lastname@example.org wrote:
> On Friday, 11 October 2013 15:27:19 UTC+2, Ben Bacarisse wrote: > > email@example.com writes: > On Thursday, 10 October 2013 16:35:29 > > > Yes, there are monotone sequences of set. Yes, what you say about them is > > rubbish. > > I only say about them that they are monotone sequences. In particilar the > finite initial segments of |N are a strictly monotonic sequence. Without any > single exception. You call that rubbish. I call it mathematics.
There are a lot more of us calling it rubbish that the one lonely idiot miscalling it mathematics.
If that were all WM said about them, we could agree, but he also says that any and ever union of such finite initial sequnces is itself a finite intiial sequence, including the union of ALL of them, which is the union of a sequence of sets which does NOT have a maximum member.
And for nested sequences of sets, like the finite initial segments of the naturals, the union of a set of them can be one of them ONLY IF there is a largest one, which occurs only if the set of them is finite.
But no finite set of naturals can be a largest possible set of naturals, Since, if finite, it will have a largest natural member and that largest member will have a natural number successor not in the set, so that that set is not maximal after all.
At least not outside of WM's wild weird world of WMytheology. --