# 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.

Is this right?
The statement is wrong how it is stated.
Consider the sawtooth wave.
Maybe you also had the condition that $f$ is continous?

3. It was a problem from a while back, so I do believe I missed the continuity part.