Convergent Sequence in a Metric Space

Definition.

Let be a sequence of points in the metric space E.

A point is called a limit of the sequence if,

given any real number ,

there is a positive integer N such that whenever .


See ita-3-3-2-page45.

1 ---------- end topic

If the sequence has a limit, we call the sequence convergent,
and if p is a limit of the sequence, we say that the sequence converges to p.

See ita-3-3-2-page45.

The statement that the sequence of points (in a metric space E)
converges to the point p (also in E)
is written concisely as
.

See ita-3-3-9-page46.