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Cauchy sequences

Cauchy sequences is the plural of Cauchy sequence.

Meaning of Cauchy sequence

Noun

Cauchy sequence (plural Cauchy sequences)

  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.
    • However, it is possible to derive topological results from statements about Cauchy sequences; for example, a subset A of the space of real numbers is closed if and only if each Cauchy sequence in A converges to some point of A.1955, [Van Nostrand], John L. Kelley, General Topology, Springer, published 1975, page 174

Questions about Cauchy sequences

What is Cauchy sequences the plural of?
Cauchy sequences is the plural of Cauchy sequence.

Words near Cauchy sequences in the dictionary

  1. Cauchy horizon
  2. Cauchy horizons
  3. Cauchy problem
  4. Cauchy problems
  5. Cauchy sequence
  6. Cauchy sequences
  7. Cauchy space
  8. Cauchy spaces
  9. Cauchy-Riemann equation
  10. Cauchy-Riemann equations
  11. Cauchy-Schwarz inequalities

Source and license

Adapted from Wiktionary: Cauchy sequences (page history and authors); Cauchy sequence (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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