In article <email@example.com>, "Julio Di Egidio" <firstname.lastname@example.org> wrote:
> That is not about proof, cardinality in terms of bijections is rather a > definition. That said, yes, I think it is sensible to say that the > collection of even natural numbers is equinumerous to that of all natural > numbers, but I have already characterised in which sense I mean that: in the > sense that both are *endless*, nothing less and nothing more.
Then do you allow sequences whose members are not members of sets? --