Definition:Periodic Function/Real

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Definition

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


Then $f$ is periodic if and only if:

$\exists L \in \R_{\ne 0}: \forall x \in \R: f \left({x}\right) = f \left({x + L}\right)$


Period

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 $L$.


Also see


Sources