A sequence over a metric space(π,π) is said to be Cauchy
iff its terms get arbitrarily close together.
More formally, a sequence (ππ)βπ=1 is a Cauchy sequence
iff. for every π>0
there exists an integer π
such that π(ππ,ππ)<π
for any π>π>π. 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.