\begin{definition}[Definition:Convergent Sequence/Metric Space/Definition 3]
Let $M = \struct {A, d}$ be a metric space or a pseudometric space.
Let $\sequence {x_k}$ be a sequence in $A$.
$\sequence {x_k}$ '''converges to the limit $l \in A$''' {{iff}}:
:$\ds \lim_{n \mathop \to \infty} \map d {x_n, l} = 0$
\end{definition}