# Cauchy sequence

(redirected from*Cauchy sequences*)

## 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}## 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).

Want to thank TFD for its existence? Tell a friend about us, add a link to this page, or visit the webmaster's page for free fun content.

Link to this page: