Is a constant function periodic? Can we regard a constant function "$f(x)=\text{constant}$" to be a periodic function? If yes, what is its period?

Nowhere in the definition of a period function is it stated that the function must have a least period.
If $f(x) = c$ then for any $p$ we have $f(x+p) = f(x)$.  So $f$ is periodic and $p$ is a period.  Obviously any other non-negative value will also be a period.
There is nothing in the definition of periodic function that says that is not allowed.
