TITLE: Is $f(x)=10$ a periodic function?
QUESTION [8 upvotes]: I am not getting satisficatory explanation for this. Clearly $f(x+T) = f(x)$ for all values of $T$.
If we assume it is periodic, does this mean period =  $0$?

REPLY [3 votes]: Yes, every constant function is periodic, and when you look at the definition of a periodic function with period T (see here) then it's easy to see that a constant is periodic with any positive number as period. So $f(x)=10$ is $n-$ periodic for every $n\in \mathbb{N}$