Definition:Periodic Real Function/Frequency

Definition
Let $f: X \to X$ be a periodic function, where $X$ is either $\R$ or $\C$.

The frequency $\nu$ of $f$ is the reciprocal of the period $L$ of $f$:
 * $\nu = \dfrac 1 L$

where:
 * $\forall x \in X: f \left({x}\right) = f \left({x + L}\right)$

where $\left|{L}\right|$ is the modulus of $L$.

Also defined as
In some contexts, the frequency of a periodic function is given by the letter $f$, but as this letter is also used for the general function, this can be seen often to be inadequate.