Definition:Periodic Function/Real

Definition
Let $f: \R \to \R$ be a real function.

Then $f$ is periodic :
 * $\exists L \in \R_{\ne 0}: \forall x \in \R: \map f x = \map f {x + L}$

Also see

 * General Periodicity Property: after every distance $L$, the function $f$ repeats itself.