Definition:Dirichlet Function
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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
- Definition:Thomae Function, also known as the Modified Dirichlet Function
- Results about Dirichlet functions can be found here.
Source of Name
This entry was named for Johann Peter Gustav Lejeune Dirichlet.
Sources
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.28$: Dirichlet ($\text {1805}$ – $\text {1859}$)