You should be able to solve this.

True or false: Are algebraic numbers countable?
You can't use axiom of choice.

>>9
A countably infinite set is one with a bijection between it and the natural numbers.
As X is countably infinite, there is a bijection f between N and X.  As f(i) is countably infinite, there is a bijection gi from N to f(i).  Let g(i,j) = gi(j).  This is a bijection from NxN to UX.