least upper bound
A number is an upper bound of a set S of numbers if every member of the set is less than or equal to it. A number n is the least upper bound of the set if there is no number less than it that is also an upper bound. It is a non-trivial result that every set of real numbers that has an upper bound has a least upper bound. If we reverse the order, considering ‘greater than or equal to’ instead of ‘less than or equal to’, we obtain the mirror notion of a greatest lower bound.

Philosophy dictionary. . 2011.

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  • least upper bound — Math. an upper bound that is less than or equal to all the upper bounds of a particular set. 3 is the least upper bound of the set consisting of 1, 2, 3. Abbr.: lub Also called supremum. * * * …   Universalium

  • least upper bound — Math. an upper bound that is less than or equal to all the upper bounds of a particular set. 3 is the least upper bound of the set consisting of 1, 2, 3. Abbr.: lub Also called supremum …   Useful english dictionary

  • 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

  • Least upper bound axiom — The least upper bound axiom, also abbreviated as the LUB axiom, is an axiom of real analysis stating that if a nonempty subset of the real numbers has an upper bound, then it has a least upper bound. It is an axiom in the sense that it cannot be… …   Wikipedia

  • upper bound — noun (mathematics) a number equal to or greater than any other number in a given set • Topics: ↑mathematics, ↑math, ↑maths • Hypernyms: ↑boundary, ↑edge, ↑bound * * * Math. an element …   Useful english dictionary

  • upper bound — Math. an element greater than or equal to all the elements in a given set: 3 and 4 are upper bounds of the set consisting of 1, 2, and 3. Cf. bound3 (def. 4), greatest lower bound, least upper bound, lower bound. * * * …   Universalium

  • Upper and lower bounds — In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set ( P , le;) is an element of P which is greater than or equal to every element of S . The term lower bound is defined dually as an element of P… …   Wikipedia

  • bound — bound1 boundness, n. /bownd/, v. 1. pt. and pp. of bind. adj. 2. tied; in bonds: a bound prisoner. 3. made fast as if by a band or bond: She is bound to her family. 4. secured within a cover, as a book. 5. under a legal or moral obligation: He is …   Universalium

  • Least mean squares filter — Least mean squares (LMS) algorithms are a class of adaptive filter used to mimic a desired filter by finding the filter coefficients that relate to producing the least mean squares of the error signal (difference between the desired and the… …   Wikipedia

  • Upper Rhine — • Ecclesiastical province; includes the Archdiocese of Freiburg and the suffragan Dioceses of Fulda, Mainz, Limburg, and Rottenburg Catholic Encyclopedia. Kevin Knight. 2006. Upper Rhine     Upper Rhine …   Catholic encyclopedia

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