Q in R/Indicator function/Nowhere continuous/Exercise

Prove that the function ${}f\colon \mathbb {R} \rightarrow \mathbb {R}$ defined by

${}f(x)={\begin{cases}1,{\text{ if }}x\in \mathbb {Q} \,,\\0\,{\text{ otherwise}}\,,\end{cases}}\,$

is for no point ${}x\in \mathbb {R}$ continuous.

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