(of a sequence in a metric space) Whose terms become arbitrarily close to one another.

A French surname; notably that of prolific mathematician Augustin-Louis Cauchy (1789-1857).

(now Guernsey) Alternative form of causey

plural of cauchie

(statistics) A symmetric continuous probability distribution with fat tails, with probability density function that is

plural of Cauchy distribution

(mathematical analysis) 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.

plural of Cauchy sequence

(topology) A space for which notions of a Cauchy sequence and completeness exist.

(mathematics, mathematical analysis) For a given m-order partial differential equation, the problem of finding a solution function u on ℝⁿ that satisfies the boundary conditions that, for a smooth manifold S⊂ℝⁿ, u(x)=f_0(x) and (∂ᵏu(x))/(∂nᵏ)=f_k(x), ∀x∈S, k=1…m-1, given specified functions f_k defined on, and vector n normal to, the manifold.