Set of points where a continuous function is Holder is Borel.

A continuous function $f:\mathbb{R}\to\mathbb{R}$ is Holder at $x$ if there exists $C,\epsilon > 0$ and $\alpha\in(0,1]$ satisfying$$|f(x)- f(y)|\leq C|x-y|^\alpha,$$ whenever $|x-y| < \epsilon.$

Show that the set of points where $f$ is Holder is a Borel set.

Honestly I'm having trouble even getting this one off the ground. Any help would be appreciated.

Thanks.