In article <firstname.lastname@example.org>, MoeBlee <email@example.com> wrote:
> On Jun 9, 10:36 am, MoeBlee <jazzm...@hotmail.com> wrote: > > > Or do you mean: > > > > S is potentially infinite <-> there exists an ordering R on X such > > that there is no R-maximal member of X > > Correction (and incorporating Virgil's remark about the empty set): > > S is potentially infinite <-> (S is non-empty & there exists a linear > ordering R on S such that there is no R-maximal member of S). > > But, isn't that equivalent with 'infinite' (i.e. 'not finite', i.e., > not equinumerous with any natural number') anyway? > > MoeBlee
It is! So if that is WM's definition, it is the same as at least one definition of actual infiniteness.