In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> Am Freitag, 6. Dezember 2013 02:42:30 UTC+1 schrieb Virgil: > > > > > > > Then the set of real remains uncountable. > > > Every infinite set remains uncountable. At least as long as mathematical > proofs are concerned.
What is WM's distinction between "countable" and of "uncountable"?
Outside of WMytheology, the definition says:
A set is countable if and only if there is a surjective mapping from the set of naturals, |N, to that set, and otherwise is uncountable.
Outside of WMytheology, that makes the set of rationals countable and the set of reals uncountable.
Inside WMytheology there could even be susets of |N which are uncountable as far as we know, because WM will never say what his definition of countability requires. --