# convergent sequence

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## fundamental sequence

- 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).

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Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018