$ \mathbb{Q} $ is countable, so we can list its elements. Let
$ \mathbb{Q} = \{r_1 , r_2, ...\}$
Define $f: \mathbb{R} \to \mathbb{R} $ by the following rule:
$ f(x) = \begin{cases} 0 & x \notin \mathbb{Q}\\ \frac{1}{n} & x=r_n \in \mathbb{Q} \end{cases}$
Find the set of discontinuities $D_f$ of $f$.
So far, I have looked at Dirichlet's function proof about how his function was discontinuous, but I don't know where to start on this one. Could someone give me a hint?