Interior Set of Rationals. Confused!

If the whole set is the $\mathbb{Q}$, then $int\mathbb{Q}=\mathbb{Q}$,

If the whole set is the $\mathbb{R}$ or $\mathbb{R}^n$, then $int\mathbb{Q}=\emptyset$,

because, $\forall q\in \mathbb{Q}, and \,\forall \epsilon>0, B_\epsilon(q)=\{x\in\mathbb{R}:|x-q|<\epsilon\}$ contains irrational numbers, which are not in the $\mathbb{Q}$, so $q$ is not a interior point of $\mathbb{Q}$.

the statement is proved.

the problem depends on the whole set you are talking about.