Enumerable and not enumerable sets I am i bit stuck on this problem. Is it possible that sets A and B are not enumerable, but set $$A \cdot B  =\{x \cdot y \mid x \in A, y \in B\}$$ is enumerable? Defenition of emumerable set so, set is enumerable if there is an algorithm, that may enumerate it. Or, set is enumerable if there is exist semi-characteristic function which equals 1 if x in A, or not define if x not in A.
Thanks in advance

If $A$ and $B$ are subsets of the real numbers and $.$ means the product, the answer is no. Indeed, since $B$ is not enumerable, it contains a non-zero number $y_0$. Then $A.B$ contains the set $A.y_0 := \{x.y_0 | x \in A\}$ which is in bijection with $A$ since $y_0$ is invertible. 
