This is pretty trivial because given countably infinite sized Turing machines (for the machine instructions to be enumerable its size must be countably infinite

This is pretty trivial because given countably infinite sized Turing machines (for the machine instructions to be enumerable its size must be countably infinite) T and countably infinite sized number of iterations N, we have the mapping f(t, n) -> x where by definition all X are the computible numbers. Since all x have at least one corresponding pair t, n, then |X| <= |T| * |N|. As T and N are countably infinite, then X must also be countably infinite by the Cantor-Bernstein theorem