I am supposed to determine whether or not the set $A\times {Z}^{+}$ where $A=\{2,3\}$ is countably infinite. If so, I should exhibit a one to one correspondence between the set of positive integers and the set in question.

Although I'm pretty sure that the set is countably infinite, I am struggling to find a one to one correspondence from the positive integers to the set since it seems to me that there are twice as many elements in the set $A\times {Z}^{+}$ than the set of positive integers since its cardinality is double due to the Cartesian product?