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# Topic: Infimum

 NationMaster - Encyclopedia: Infimum The supremum is given by the union and the infimum by the intersection of subsets. The infimum is given by the intersection of convex sets and the supremum by the convex hull of the union. The infimum is given by the intersection of topologies, and the supremum by the topology generated by the union of topologies. www.nationmaster.com /encyclopedia/Infimum   (1475 words)

 PlanetMath: infimum Also note that a set does not necessarily have an infimum. See Also: supremum, Lebesgue outer measure, minimal and maximal number, infimum and supremum for real numbers This is version 5 of infimum, born on 2001-10-18, modified 2002-11-25. planetmath.org /encyclopedia/Infimum.html   (93 words)

 subset, partially, article, mathbb, least, concept, arbitrary, about - Infimum In mathematics the infimum of a subset of some set is the greatest element, not necessarily in the subset, that is smaller than all other elements of the subset. In analysis the infimum or greatest lower bound of a set S of real numbers is denoted by inf(S) and is defined to be the biggest real number that is smaller than or equal to every number in S. The notions of infimum and supremum are dual in the sense that www.alphasearch.org /Infimum.html   (674 words)

 Lattice The supremum is given by the union and the infimum by the intersection of subsets. The infimum is given by the intersection of convex sets and the supremum by the convex hull of the union. The infimum is given by the intersection of topologies, and the supremum by the topology generated by the union of topologies. www.ebroadcast.com.au /lookup/encyclopedia/la/Lattice.html   (913 words)

 MySQL AB :: MySQL Internals Manual :: 12.2.1.3 The Infimum and Supremum Records   (Site not responding. Last check: ) , an infimum is lower than the lowest possible real value (negative infinity) and a supremum is greater than the greatest possible real value (positive infinity). Also, the infimum record can be a dummy target for temporary record locks. considers the infimum and supremum to be part of the header or not. dev.mysql.com /doc/internals/en/innodb-infimum-and-supremum-records.html   (184 words)

 Wikinfo | Infimum In analysis the infimum or greatest lower bound of a set S of real numbers is denoted by inf(S) and is defined to be the biggest real number that is smaller than or equal to every number in S. If the infimum value belongs to the set then we can say there is a smallest element in the set. A infimum or greatest lower bound of S is an element l in P such that www.wikinfo.org /wiki.php?title=Infimum   (491 words)

 CMIS Research - Image Analysis Activities - Recent Projects - Colour Morphology The infimum of a set of images is defined as the greatest lower bound of the images, which for binary images is simply the pixel-wise minimum of the images. For example, the infimum of 1 0 0 and 1 1 0 is 1 0 0 and the infimum of 1 1 0 and 0 1 1 is 0 1 0. Similarly, the infimum would be red and not a mixture of the two colours. www.cmis.csiro.au /iap/RecentProjects/colour.htm   (1997 words)

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