minimal and maximal number

Let’s consider a finite non-empty set  A={a1,,an}   of real numbers or an infinite but compact (i.e. bounded and closed) set A of real numbers.  In both cases the set has a unique least number and a unique greatest number.

  • The least number of the set is denoted by  min{a1,,an}  or  minA.

  • The greatest number of the set is denoted by  max{a1,,an}  or  maxA.

In both cases we have


where  infA  and  supA  are the infimum and supremum of the set A.

The min and max are set functions, i.e. they map subsets of a certain set to .

The min and max have the following distributive properties with respect to addition:


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 InfimumPlanetmathPlanetmath
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 InterprimeMathworldPlanetmath
Related topic LehmerMean
Related topic Ab
Defines least number
Defines greatest number
Defines minimal number
Defines maximal number
Defines set function