Questions on periodic functions, functions $f(x)$ that satisfy the identity $f(x+c)=f(x)$, for some nonzero $c$.

A periodic function is a non-constant function that repeats itself in regular intervals, i.e. one satisfying $f(x+c)=f(x)$. The least such $c$ is called the period of $f$.

Graphically, you can see periodicity through translational symmetry. You can see this most easily with trigonometric functions like $\sin$ and $\cos$, which have period $2\pi$. Still, several well-known functions such as Thomae's function which is periodic with period one, cannot accurately be graphed. Other examples of periodic functions include sawtooth and square waves and division with a fixed modulus, e.g. $f(x)= x\bmod 10$.

Periodic functions are perhaps best known through Fourier series. A function that is integrable over an interval of length $L$ can be periodically extended into a Fourier series with period $L$.