\begin{definition}[Definition:Continuous Complex Function/Using Limit]
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}}:
:The limit of $\map f z$ as $z \to a$ exists, and
:$\ds \lim_{z \mathop \to a} \map f z = \map f a$
Category:Definitions/Complex Analysis
\end{definition}