Prove or disprove that $\mathbb{Q}-\mathbb{Z}$ is denumerable My question states: prove or disprove that $\mathbb{Q}-\mathbb{Z}$ is denumerable.

$\mathbb Q - \mathbb Z \subset \mathbb Q$. $\mathbb Q$ is denumerable, and so is any subset of it. More generally, any subset of a denumerable set is denumerable.