Cauchy sequence

Cauchy sequence
noun Etymology: Augustin-Louis Cauchy died 1857 French mathematician Date: circa 1949 a sequence of elements in a metric space such that for any positive number no matter how small there exists a term in the sequence for which the distance between any two terms beyond this term is less than the arbitrarily small number

New Collegiate Dictionary. 2001.

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  • Uniformly Cauchy sequence — In mathematics, a sequence of functions {f {n}} from a set S to a metric space M is said to be uniformly Cauchy if:* For all xin S and for all varepsilon > 0, there exists N>0 such that d(f {n}(x), f {m}(x)) < varepsilon whenever m, n > N.Another …   Wikipedia

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  • Cauchy net — In mathematics, a Cauchy net generalizes the notion of Cauchy sequence to nets defined on uniform spaces.A net ( x α) is a Cauchy net if for every entourage V there exists γ such that for all α, β ≥ γ, ( x α, x β) is a member of V . More… …   Wikipedia

  • Cauchy's convergence test — The Cauchy convergence test is a method used to test infinite series for convergence. A series:sum {i=0}^infty a iis convergent if and only if for every varepsilon>0 there is a number N inmathbb{N} such that:|a {n+1}+a {n+2}+cdots+a {n+p}|0 there …   Wikipedia

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