English Explanatory Dictionary

Cauchy sequence

English dictionary entry

Meanings

noun
  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.

Word forms

Cauchy sequence Cauchy sequences

Etymology

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

Related words

Cauchy convergence Cauchy filter Cauchy net Cauchy space

Derived words

Cauchy
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