# Dirichlet function

The Dirichlet function $D \colon \mathbb{R} \rightarrow \{0,1\}$ is defined by $$D(x) = \left\{ \begin{array}{ll} 1, & y \in \mathbb{Q} \\ 0, & y \in \mathbb{R} \setminus \mathbb{Q}, \end{array} \right.$$ where $\mathbb{Q}$ denotes the set of rational numbers and $\mathbb{R} \setminus \mathbb{Q}$ denotes the set of irrational number.