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Infimum and supremum

In mathematics, the infimum (abbreviated inf; pl.: infima) of a subset S {\displaystyle S} of a partially ordered set P {\displaystyle P} is the greatest element in P {\displaystyle P} that is less than or equal to each element of S , {\displaystyle S,} if such an element exists. If the infimum of S {\displaystyle S} exists, it is unique, and if b is a…

Art, Infima and suprema of real numbers & Examples

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Overview

Formal definition

Existence and uniqueness

Relation to maximum and minimum elements

Infima and suprema of real numbers

Duality

Examples

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Infimum and supremum

Nodes58
Edges57
Triples17
Avg. degree1.97
Density0.034483
Components1

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Infimum and supremum

Top relations

related to External links · 10
Infimum and supremum → Breitenbach, EMS Press, Encyclopedia, Eric, Infimum, Jerome, Mathematics, MathWorld, Upper, Weisstein
see also · 7
Infimum and supremum → Bounds, Concept, Essential, Extreme, Infimum, Majorant, Upper

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Important terminology

displaystyle set numbers real supremum sup infimum bound inf subset upper mathbb element ordered least sets also number partially greatest

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Infimum and supremumrelated to External linksUpper0.60section
Infimum and supremumrelated to External linksEncyclopedia0.60section
Infimum and supremumrelated to External linksMathematics0.60section
Infimum and supremumrelated to External linksEMS Press0.60section
Infimum and supremumrelated to External linksBreitenbach0.60section
Infimum and supremumrelated to External linksJerome0.60section
Infimum and supremumrelated to External linksWeisstein0.60section
Infimum and supremumrelated to External linksEric0.60section
Infimum and supremumrelated to External linksInfimum0.60section
Infimum and supremumrelated to External linksMathWorld0.60section
Infimum and supremumsee alsoEssential0.60section
Infimum and supremumsee alsoInfimum0.60section

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    Min side: 3
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