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

${\displaystyle f\colon \mathbb {R} \longrightarrow \mathbb {R} }$
${\displaystyle {}f(x)={\begin{cases}x,\,{\text{ if }}x\in \mathbb {Q} \,,\\0,\,{\text{ otherwise}}\,,\end{cases}}\,}$
is only at the zero point ${\displaystyle {}0}$ continuous.