\begin{definition}[Definition:Convergent Mapping/Complex Function]
Let $f: \C \to \C$ be a complex function defined everywhere on $\C$ ''except possibly'' at $c$.
Let $f \left({z}\right)$ tend to the limit $L$ as $z$ tends to $c$.
Then $f$ '''converges to the limit $L$ as $z$ tends to $c$'''.
\end{definition}