# Math Help - Are periodic functions uniformly continuous?

1. ## Are periodic functions uniformly continuous?

I think it is, here is my proof:

Suppose that $f: \mathbb {R} \mapsto \mathbb {R}$ is a t-periodic function. We will show that f is uniformly continuous.

Let $\epsilon > 0$, find $\delta > t$ such that $x \in \mathbb {R}$ with $y = x + t$, then $|x-y| = | x - x + t | = |-t| = t < \delta$

We then have $|f(x) - f(y) | = |f(x) - f(x + t)| = |f(x)-f(x)| =0 < \epsilon$, thus proves the claim.

Is this right? Thank you.

Maybe you also had the condition that $f$ is continous?