Earlier quoted context omitted.
> The problem is that while a superset of an uncountable set is uncountable, a superset of a computably uncountable set may instead be computably countable. The partial functions over the integers show that this is indeed the case. > The computable countability of the partial maps from N to N. Can anybody give an example? does this have any to do with rationals? or is it more related to limits and calculus?
> does this have any to do with rationals? or is it more related to limits and calculus? No. I'm going to use Haskell, which I'm going to assume you know. I'm using it because it seems closer to the math. The type for naturals is: data Nat = Zero | Succ Nat and then all Haskell functions of type `Nat -> Nat` represent partial functions. They're not total functions because they might enter an infinite loop for some in…
Is this a finite process?