In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 26 Okt., 18:42, William Hughes <wpihug...@gmail.com> wrote: > > > Incorrect. All other elements are sets with > > a largest element. b_oo is a set without a largest element. > > Sets are defined by elements, not by missing elements.
Sets can be distinguished by elements missing from one but not another.
And these are ordered sets which can be distinguished by having different order properties even when they were to have exacly the same elements. > > > There is no element in b_oo that distinguishes it from > > all the other elements. > > Small wonder because b_oo does not exist.
Perhaps not in WM's matheology, but in real math it can and does.
> > > That does not mean b_oo cannot be > > distinguished from all the other elements. > > Just that is meant.
You mean that b_1 and b_oo are indistiguishable, and also b_2 and b_00 are indistiguishable?
Does that not imply that b_1 and b_2 are also indistinguishable?
> > You can easily recognize that your position has broken down by the > following: > > The limit of the sequence of sets > (1) > (1,2) > (1,2,3) > ... > is |N. > > The limit of the sequence of sets > (1) > (2,3) > (4,5,6) > ... > is the empty set.
Actually, it is not defined at all, which is not at all the same as being the empty set.