Phrase guide

Cauchy sequence

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 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.

Definition source: English Wiktionary via Wiktextract

Topics: mathematical-analysis, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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

Across languages

Translations

10 source translations are retained for this English entry.

  • Bulgarian: редица на Коши (redica na Koši) — sequence in a normed vector space
  • Danish: Cauchyfølge — sequence in a normed vector space
  • Finnish: Cauchyn jono — sequence in a normed vector space
  • French: suite de Cauchy — sequence in a normed vector space
  • German: Cauchy-Folge — sequence in a normed vector space
  • German: Cauchyfolge — sequence in a normed vector space
  • Italian: successione di Cauchy — sequence in a normed vector space
  • Polish: ciąg Cauchy'ego — sequence in a normed vector space
  • Serbo-Croatian: Cauchyjev niz — sequence in a normed vector space
  • Swedish: Cauchyföljd — sequence in a normed vector space