cauchy sequence
51Absolute value (algebra) — In mathematics, an absolute value is a function which measures the size of elements in a field or integral domain. More precisely, if D is an integral domain, then an absolute value is any mapping | thinsp; sdot; thinsp;| from D to the real… …
52Limit (mathematics) — This is an overview of the idea of a limit in mathematics. For specific uses of a limit, see limit of a sequence and limit of a function. In mathematics, the concept of a limit is used to describe the value that a function or sequence approaches… …
53Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …
54metric space — Math. a space with a metric defined on it. [1925 30] * * * In mathematics, a set of objects equipped with a concept of distance. The objects can be thought of as points in space, with the distance between points given by a distance formula, such… …
55Constructivism (mathematics) — In the philosophy of mathematics, constructivism asserts that it is necessary to find (or construct ) a mathematical object to prove that it exists. When one assumes that an object does not exist and derives a contradiction from that assumption,… …
56Alternating series — In mathematics, an alternating series is an infinite series of the form:sum {n=0}^infty ( 1)^n,a n,with an ≥ 0 (or an ≤ 0) for all n . A finite sum of this kind is an alternating sum. An alternating series converges if the terms an converge to 0… …
57Uniform continuity — In mathematical analysis, a function f ( x ) is called uniformly continuous if, roughly speaking, small changes in the input x effect small changes in the output f ( x ) ( continuity ), and furthermore the size of the changes in f ( x ) depends… …
58Banach space — In mathematics, Banach spaces (pronounced [ˈbanax]) is the name for complete normed vector spaces, one of the central objects of study in functional analysis. A complete normed vector space is a vector space V with a norm ||·|| such that every… …
59Completeness — In general, an object is complete if nothing needs to be added to it. This notion is made more specific in various fields. Contents 1 Logical completeness 2 Mathematical completeness 3 Computing 4 …
60Generalized continued fraction — In analysis, a generalized continued fraction is a generalization of regular continued fractions in canonical form in which the partial numerators and the partial denominators can assume arbitrary real or complex values.A generalized continued… …
