# Liouville's Theorem

Let f be an entire function in the complex plane. Show that if f is constant on a non-empty open set U ⊆ $\mathbb{C}$ then f is constant on $\mathbb{C}$

I think this is a Liouville's theorem question but I don't know how to incorporate it in a formal proof.

• If it more like identity principle. If $f$ is constant on an open then its Taylor series at a point in that open is constant. Finally, Cauchy's theorem tells you that that series converges to the function everywhere. – OR. Apr 3 '15 at 1:07