Math. an infinite sequence, x1, x2, …, whose terms are points in Ek, in which there exists a point y such that the limit as n goes to infinity of xn = y if and only if for every ε>0, there exists a number N such that i>N and j>N implies |xi -xj|< ε. Also called Cauchy sequence, convergent sequence. Cf. complete (def. 10b).