# fundamental sequence

nounMathematics.

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.

## Origin of fundamental sequence

^{1}

First recorded in 1865–70

- Also called Cauchy sequence, convergent sequence .

- Compare complete (def. 10b).

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2024

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