Cauchy sequence
Definition from Wiktionary, the free dictionary
English[edit]
Noun[edit]
Cauchy sequence (plural Cauchy sequences)
 (analysis) A sequence in a normed vector space such that the difference between any two entries can be made arbitrarily small by stipulating that the two entries be sufficiently far out in the sequence.
 (analysis) A sequence in a metric space with metric d such that for every there exists a natural number N so that for every : .
 2000, George Bachman, Lawrence Narici, Functional Analysis, page 52,
 In the case of the real line, every Cauchy sequence converges; that is, being a Cauchy sequence is sufficient to guarantee the existence of a limit. In the general case, however, this is not so. If a metric space does have the property that every Cauchy sequence converges, the space is called a complete metric space.
 2000, George Bachman, Lawrence Narici, Functional Analysis, page 52,
Translations[edit]
sequence in a normed vector space

