# Is $f(x)=10$ a periodic function?

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 = $0$?

• It just means that it is periodic for any value of $T$. – Daniel Aug 23 '14 at 16:57
• en.wikipedia.org/wiki/Periodic_function – Surb Aug 23 '14 at 16:57
• We do not normally consider $0$ to be a possible period of a periodic function; if we did, then every function would be periodic. – MJD Nov 1 '14 at 20:52
• – Przemysław Scherwentke Nov 8 '14 at 3:17

• $$\text{Harry Potter shouts: The minimum period is h tends to zero!}\\ \text{Dumbledore retorts: ... or }\frac{1}{\infty}$$ – Nick Aug 23 '14 at 17:10
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 $n\in \mathbb{N}$
• No need to restrict $n$ to $\Bbb N$; it is periodic for every $n\in \Bbb R$, in fact. – MJD Aug 23 '14 at 17:02