2. Proposition 2.2.1

Let $U \subseteq C$ open, $z_{0} \in U$ , and $f : U \to C$ be holomorphic. Further suppose that $z_{0}$ is a zero of $f$ of infinite order. Then there exists $r > 0$ such that 1;; $f (z) = 0$ for all $z \in B_{r} (z_{0})$