fundamental sequence

noun Mathematics.

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.Compare complete(def 10b).