\begin{definition}[Definition:Continuous Complex Function/Epsilon-Delta]
Let $A_1, A_2 \subseteq \C$ be subsets of the complex plane.
Let $f: A_1 \to A_2$ be a complex function from $A_1$ to $A_2$.
Let $a \in A_1$.
$f$ is '''continuous at (the point) $a$''' {{iff}}:
:$\forall \epsilon > 0: \exists \delta > 0: \forall z \in A_1: \cmod {z - a} < \delta \implies \cmod {\map f z - \map f a} < \epsilon$
Category:Definitions/Complex Analysis
\end{definition}