# Definition:Dirichlet Function

## Definition

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 $d = 0$.

## Also see

• Results about Dirichlet functions can be found here.

## Source of Name

This entry was named for Johann Peter Gustav Lejeune Dirichlet.