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 defined as
Some sources define a periodic real function as one such that:


 * $\exists L \in \R_{\ne 0}: \forall x \in \R: \map f x = \map f {x + 2 L}$

In some circumstances it can make the algebra simpler to define the period as being $2$ times a specified constant.

Also see

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