minimal and maximal number
Let’s consider a finite non-empty set of real numbers or an infinite but compact (i.e. bounded and closed) set of real numbers. In both cases the set has a unique least number and a unique greatest number.
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The least number of the set is denoted by or .
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The greatest number of the set is denoted by or .
In both cases we have
where and are the infimum and supremum of the set .
The and are set functions, i.e. they map subsets of a certain set to .
The minimal and maximal number of a set of two real numbers obey the formulae
Title | minimal and maximal number |
Canonical name | MinimalAndMaximalNumber |
Date of creation | 2014-02-15 18:33:33 |
Last modified on | 2014-02-15 18:33:33 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 25 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 26B12 |
Classification | msc 03E04 |
Synonym | least and greatest number |
Related topic | Infimum |
Related topic | Supremum |
Related topic | UltrametricTriangleInequality |
Related topic | GrowthOfExponentialFunction |
Related topic | EstimatingTheoremOfContourIntegral |
Related topic | LeastAndGreatestValueOfFunction |
Related topic | FuzzyLogic2 |
Related topic | ZerosAndPolesOfRationalFunction |
Related topic | UniformConvergenceOnUnionInterval |
Related topic | Interprime |
Related topic | LehmerMean |
Related topic | Ab |
Defines | least number |
Defines | greatest number |
Defines | minimal number |
Defines | maximal number |
Defines | set function |