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bounded above subset

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  • Bounded set — In mathematical analysis and related areas of mathematics, a set is called bounded, if it is, in a certain sense, of finite size. Conversely a set which is not bounded is called unbounded. Definition A set S of real numbers is called bounded from …   Wikipedia

  • Bounded variation — In mathematical analysis, a function of bounded variation refers to a real valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense. For a continuous function of a… …   Wikipedia

  • Bounded complete poset — In the mathematical field of order theory, a partially ordered set is bounded complete if all of its subsets which have some upper bound also have a least upper bound. Such a partial order can also be called consistently complete, since any upper …   Wikipedia

  • Totally bounded space — In topology and related branches of mathematics, a totally bounded space is a space that can be covered by finitely many subsets of any fixed size (where the meaning of size depends on the given context). The smaller the size fixed, the more… …   Wikipedia

  • Resource bounded measure — Lutz s resource bounded measure is a generalisation of Lebesgue measure to complexity classes. It was originally developed by Jack Lutz. Just as Lebesgue measure gives a method to quantify the size of subsets of the Euclidean space R^n, resource… …   Wikipedia

  • Linear continuum — In the mathematical field of order theory, a continuum or linear continuum is a generalization of the real line. Formally, a linear continuum is a linearly ordered set S of more than one element that is densely ordered , i.e., between any two… …   Wikipedia

  • Compact space — Compactness redirects here. For the concept in first order logic, see compactness theorem. In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness… …   Wikipedia

  • Big O notation — In mathematics, big O notation is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is… …   Wikipedia

  • Supremum — In mathematics, given a subset S of a partially ordered set T , the supremum (sup) of S , if it exists, is the least element of T that is greater than or equal to each element of S . Consequently, the supremum is also referred to as the least… …   Wikipedia

  • Extreme value theorem — This article is about continuous functions in analysis. For statistical theorems about the largest observation in a sequence of random variables, see extreme value theory. A continuous function ƒ(x) on the closed interval [a,b] showing the… …   Wikipedia

  • Integral — This article is about the concept of integrals in calculus. For the set of numbers, see integer. For other uses, see Integral (disambiguation). A definite integral of a function can be represented as the signed area of the region bounded by its… …   Wikipedia

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