# Cauchy sequence

> English word · Noun

## Definitions
1. Any sequence x_n in a metric space with metric d such that for every ϵ>0 there exists a natural number N such that for all k,m>N, d(x_k,x_m)<ϵ.

## Etymology
Named after French mathematician Augustin-Louis Cauchy (1789–1857), who made pioneering contributions to analysis.

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/cauchy-sequence