4. periodicity

A function f is said to be periodic with a period T if, for some nonzero constant T, we have: f(x + T) = f(x) for all values of x. If there exists a least positive constant T with this property, it is called the prime period. A function with period T will repeat on intervals of length T, and these intervals are sometimes also referred to as periods.

Example: f(x) = sin x, is a periodic function and its prime period is T = 2π

sin (x + 2π) = sin x