In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> I did not say that there is a final step. I say that there is no > chance for a difference of lim card(S_n) and card(lim(S_n)) where lim > means n --> oo.
But "lim" requires a deal more than merely "n --> oo". In each case, "lim_[n --> oo] card(S_n)" and "card( lim_[n --> oo](S_n))", one has to say under what conditions the alleged limit will actually exist and how its value is determined when it does exist.
And with Dik's definitions, the two limits need not be equal.