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least-upper-bound theorem

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  • Least-upper-bound property — In mathematics, the least upper bound property is a fundamental property of the real numbers and certain other ordered sets. The property states that any non empty set of real numbers that has an upper bound necessarily has a least upper bound… …   Wikipedia

  • Theorem — The Pythagorean theorem has at least 370 known proofs[1] In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements …   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

  • Knaster–Tarski theorem — In the mathematical areas of order and lattice theory, the Knaster–Tarski theorem, named after Bronisław Knaster and Alfred Tarski, states the following:: Let L be a complete lattice and let f : L → L be an order preserving function. Then the set …   Wikipedia

  • Intermediate value theorem — In mathematical analysis, the intermediate value theorem states that for each value between the upper and lower bounds of the image of a continuous function there is a corresponding value in its domain mapping to the original.Intermediate value… …   Wikipedia

  • Monotone convergence theorem — In mathematics, there are several theorems dubbed monotone convergence; here we present some major examples. Contents 1 Convergence of a monotone sequence of real numbers 1.1 Theorem 1.2 Proof 1.3 …   Wikipedia

  • Bolzano–Weierstrass theorem — In real analysis, the Bolzano–Weierstrass theorem is a fundamental result about convergence in a finite dimensional Euclidean space R^n. The theorem states that each bounded sequence in R^n has a convergent subsequence. An equivalent formulation… …   Wikipedia

  • Cauchy-Hadamard theorem — In mathematics, the Cauchy Hadamard theorem is a result in complex analysis named after the French mathematicians Augustin Louis Cauchy and Jacques Hadamard.tatement of the theoremConsider the formal power series in one complex variable z of the… …   Wikipedia

  • intermediate value theorem — noun a statement that claims that for each value between the least upper bound and greatest lower bound of the image of a continuous function there is a corresponding point in its domain that the function maps to that value …   Wiktionary

  • Nyquist–Shannon sampling theorem — Fig.1: Hypothetical spectrum of a bandlimited signal as a function of frequency The Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, is a fundamental result in the field of information theory, in particular… …   Wikipedia

  • Ramsey's theorem — This article goes into technical details quite quickly. For a slightly gentler introduction see Ramsey theory. In combinatorics, Ramsey s theorem states that in any colouring of the edges of a sufficiently large complete graph (that is, a simple… …   Wikipedia

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