Cauchy sequence

A sequence over a metric space is said to be Cauchy iff its terms get arbitrarily close together. More formally, a sequence is a Cauchy sequence iff. for every there exists an integer such that for any . anal

It is easy to prove that every convergent sequence is a Cauchy sequence using the triangle inequality. A metric space in which every convergent sequence is a Cauchy sequence is called a Complete metric space.