# Cauchy sequence

(redirected from Cauchy sequences)
Also found in: Wikipedia.

## 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 {an } such that for every ε > 0 there is an integer N with the property that, if n and m are both greater than N, then | an-am | < ε.="" also="" known="" as="" fundamental="" sequence;="" regular="">

## 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).
References in periodicals archive ?
1,l]) (k,l [less than or equal to] r) are Cauchy sequences in (X,q).
m] are technically equivalence classes of Cauchy sequences of elements of [[?
122) that there exist Cauchy sequences which are not Mackey-Cauchy sequences.
For more generality, we can replace the condition of closedness of T by the following condition: T is a nonempty subset of R such that every Cauchy sequence in T converges to a point of T with the possible exception of Cauchy sequences which converge to a finite infimum or finite supremum of t.

Site: Follow: Share:
Open / Close