Definition:Convergent Sequence/Metric Space/Definition 3

Definition
Let $M = \struct {A, d}$ be a metric space or a pseudometric space.

Let $\sequence {x_k}$ be a sequence in $A$.

Then $\sequence {x_k}$ converges to the limit $l \in A$ :
 * $\displaystyle \lim_{n \mathop \to \infty} \map d {x_n, l} = 0$

Also see

 * Equivalence of Definitions of Convergent Sequence in Metric Space