Real function/Identity on Q/Else 0/Continuous in 0/Exercise

Prove that the function

$f\colon \mathbb {R} \longrightarrow \mathbb {R}$

defined by

${}f(x)={\begin{cases}x,\,{\text{ if }}x\in \mathbb {Q} \,,\\0,\,{\text{ otherwise}}\,,\end{cases}}\,$

is only at the zero point ${}0$ continuous.

Create a solution