\begin{definition}[Definition:Convergent Sequence/Complex Numbers/Definition 1]
Let $\sequence {z_k}$ be a sequence in $\C$.
$\sequence {z_k}$ '''converges to the limit $c \in \C$''' {{iff}}:
:$\forall \epsilon \in \R_{>0}: \exists N \in \R: n > N \implies \cmod {z_n - c} < \epsilon$
where $\cmod z$ denotes the modulus of $z$.
\end{definition}