General Periodicity Property

Theorem
Let $f: X \to X$ be a periodic function, where $X$ is either the set of real numbers $\R$ or the set of complex numbers $\C$.

Let $L$ be the period of $f$.

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

That is, after every distance $L$, the function $f$ repeats itself.