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