\begin{definition}[Definition:Dirichlet Function]
A '''Dirichlet function''' $D: \R \to \R$ is a real function defined as:
:$\forall x \in \R: \map D x = \begin {cases} c & : x \in \Q \\ d & : x \notin \Q \end {cases}$
for $c, d \in \R$ such that $c \ne d$.
The canonical example of this has $c = 1$ and $d = 0$.
\end{definition}