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Cauchy sequence — In mathematics, a Cauchy sequence, named after Augustin Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses. To be more precise, by dropping enough (but still only a finite number of) terms from… … Wikipedia
cauchy sequence — ˈkōshē , kōˈshē noun Usage: usually capitalized C Etymology: after Augustin Louis Cauchy died 1857 French mathematician : a sequence of elements in a metric space such that for any positive number no matter how small there exists a term in the… … Useful english dictionary
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… … New Collegiate Dictionary
Cauchy sequence — Math. See fundamental sequence. [named after A. L. CAUCHY] * * * … Universalium
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
Cauchy-continuous function — In mathematics, a Cauchy continuous, or Cauchy regular, function is a special kind of continuous function between metric spaces (or more general spaces). Cauchy continuous functions have the useful property that they can always be (uniquely)… … Wikipedia
Sequence — For other uses, see Sequence (disambiguation). In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements or terms), and the number of terms (possibly infinite) is called the length … Wikipedia
Cauchy space — In general topology and analysis, a Cauchy space is a generalization of metric spaces and uniform spaces for which the notion of Cauchy convergence still makes sense. Cauchy spaces were introduced by H. H. Keller in 1968, as an axiomatic tool… … Wikipedia
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
