This recently came up to me, can a constant function be considered periodic in a sense that it has infinite number of periods since
$$f(x+k)=c=f(x)$$ for $k\in(-\infty,\infty)$ ?
If this were true, for the graph of $f(x)$ to remain a straight line everywhere, the frequency of the function must be reaching infinity (invalidating the claim that there are infinite number of periods) with an amplitude that approaches $0$. How do I make sense out of this