\begin{definition}[Definition:Isolated Singularity/Pole]
Let $U$ be an open subset of a Riemann surface.
Let $z_0 \in U$.
Let $f: U \setminus \set {z_0} \to \C$ be a holomorphic function.
Let $z_0$ be an isolated singularity of $f$.
Then $z_0$ is a '''pole''' {{iff}}:
:$\ds \lim_{z \mathop \to z_0} \cmod {\map f z} \to \infty$
\end{definition}