>Cantor's diagonal proof does *not* show the Reals are uncountable; it just >proves the much weaker statement that "the Reals cannot be listed".
Those two statements mean the *same* thing!
A "list" of objects is just a function that maps each natural number to an object. To say that a set is listable is just to say that there exists a list that contains all objects in the set. And that's exactly what it means to say that a set is countable.