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

Prove that the function

$f:ℝ⟶ℝ$

defined by

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

is only at the zero point $0$ continuous.

Create a solution