# Definition:Periodic Function/Period

## Definition

Let $f: X \to X$ be a periodic function, where $X$ is either $\R$ or $\C$.

The period of $f$ is the smallest value $\cmod L \in \R_{\ne 0}$ such that:

$\forall x \in X: \map f x = \map f {x + L}$

where $\cmod L$ is the modulus of $L$.