# Definition:Antiperiodic Function/Real

## Definition

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

Then $f$ is anti-periodic if and only if:

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

### Antiperiod

The antiperiod 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 $L$.