Definition:Periodic Real Function/Period

Definition

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

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

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

Also defined as

Some sources define a period of a periodic function $f$ as any $L \in \R_{>0}$ such that $\forall x \in \R: \map f x = \map f {x + L}$, not necessarily the smallest.

Also known as

The period of a periodic function $f$ is also known as the principal period of $f$, particularly by those sources which define a period of $f$ as any $L \in \R_{>0}$ such that:

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