Definition:Convergent Sequence

Metric Space
For other equivalent definitions of a convergent sequence in a Metric Space see: Definition:Convergent Sequence in Metric Space

Standard Number Fields
When $A$ is one of the standard number fields $\Q, \R, \C$, and the metric $d$ is the usual (Euclidean) metric, the condition on convergence becomes:

Also known as
A convergent sequence is also known by its variant converging sequence.

In the interests of consistency, the latter term is avoided on.

Also see

 * Definition:Divergent Sequence: a sequence which is not convergent