In article <QP-dnV0EIYPt2b3WnZ2dnUVZ_h2dnZ2d@giganews.com>, "K_h" <KHolmes@SX729.com> wrote:
> "Virgil" <Virgil@home.esc> wrote in message > news:Virgil-1E8B09.email@example.com... > > In article > > <c8idnc6JG6hv34LWnZ2dnUVZ_q-dnZ2d@giganews.com>, > > "K_h" <KHolmes@SX729.com> wrote: > > > >> It should be pointed out that N is a limit set even if N > >> is > >> initially given by a definition that doesn't involve the > >> notion of a limit. > > > > > > The issue between Dik and WM is whether the limit of a > > sequence of sets > > according to Dik's definition of such limits is > > necessarily the same as > > the limit of the sequence of cardinalities for those sets. > > > > And Dik quire successfully gave an example in which the > > limits differ. > > I suspect those definitions are not valid.
Irrelevant to whether that definition "is valid" or corresponds to anyone else's. That is the definition under which WM claimed the two limit processes coincide, but they do not.