Cauchy sequence


Cauchy sequence

[kō·shē ′sē·kwəns] (mathematics) A sequence with the property that the difference between any two terms is arbitrarily small provided they are both sufficiently far out in the sequence; more precisely stated: a sequence {an } such that for every ε > 0 there is an integer N with the property that, if n and m are both greater than N, then | an-am | < ε.="" also="" known="" as="" fundamental="" sequence;="" regular="">

Cauchy sequence

(mathematics)A sequence of elements from some vector spacethat converge and stay arbitrarily close to each other (usingthe norm definied for the space).