 Regular Cauchy sequences were used by Errett Bishop in his Foundations of Constructive Analysis, and by Douglas Bridges in a non-constructive textbook ().Since the definition of a Cauchy sequence only involves metric concepts, it is straightforward to generalize it to any metric space "X".To do so, the absolute value |"x""m" - "x""n"| is replaced by the distance "d"("x""m", "x""n") (where "d" denotes a metric) between "x""m" and "x""n".