\begin{definition}[Definition:Limit of Sequence/Metric Space]
Let $M = \struct {A, d}$ be a metric space or pseudometric space.
Let $\sequence {x_n}$ be a sequence in $M$.
Let $\sequence {x_n}$ converge to a value $l \in A$.
Then $l$ is a '''limit of $\sequence {x_n}$ as $n$ tends to infinity'''.
If $M$ is a metric space, this is usually written:
:$\ds l = \lim_{n \mathop \to \infty} x_n$
\end{definition}