# Cauchy sequence

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## Cauchy sequence

[kō·shē ′sē·kwəns] (mathematics)

A sequence with the property that the difference between any two terms is arbitrarily small provided they are both sufficiently far out in the sequence; more precisely stated: a sequence {

*a*} such that for every ε > 0 there is an integer_{n}*N*with the property that, if*n*and*m*are both greater than*N*, then |*a*-_{n}*a*| < ε.="" also="" known="" as="" fundamental="" sequence;="" regular="">_{m}McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## Cauchy sequence

(mathematics)A sequence of elements from some vector space
that converge and stay arbitrarily close to each other (using
the norm definied for the space).

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