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Indicator function

In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if A is a subset of some set X, then the indicator function of A is the function 1 A {\displaystyle \mathbf {1} _{A}} defined by 1 A ( x ) = 1 {\displaystyle \mathbf {1}…

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Basic properties

MapsCodomainSurjectiveProper subsetComplement
17 related topics

Smoothness

SupportConnected componentAlgebraic geometryFinite fieldsAffine variety
16 related topics

Characteristic function in fuzzy set theory

Fuzzy set theoryAlgebraStructurePosetLattice
8 related topics

Notation and terminology

Characteristic functionConvex analysisReciprocalStatisticsDummy variable
11 related topics

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Overview

Notation and terminology

Basic properties

Mean, variance and covariance

Characteristic function in recursion theory, Gödel's and Kleene's representing function

Characteristic function in fuzzy set theory

Smoothness

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Indicator function

Nodes75
Edges74
Triples15
Avg. degree1.97
Density0.026667
Components1

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Indicator function

Top relations

related to Smoothness · 10
Indicator function → Although, Dirac, For, Given, Heaviside, If, In, The, Then, Zariski
related to Definition · 2
Indicator function → Given, The Iverson
related to Notation and terminology · 2
Indicator function → The, This
is a · 1
Indicator function → useful notational device in combinatorics

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Important terminology

function displaystyle indicator mathbf set characteristic mathbb subset functions theory left operatorname defined right bigl bigr derivative delta representing fuzzy

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Indicator functionis auseful notational device in combinatorics0.90text
Indicator functionrelated to DefinitionGiven0.60section
Indicator functionrelated to DefinitionThe Iverson0.60section
Indicator functionrelated to Notation and terminologyThe0.60section
Indicator functionrelated to Notation and terminologyThis0.60section
Indicator functionrelated to SmoothnessIn0.60section
Indicator functionrelated to SmoothnessZariski0.60section
Indicator functionrelated to SmoothnessGiven0.60section
Indicator functionrelated to SmoothnessThen0.60section
Indicator functionrelated to SmoothnessIf0.60section
Indicator functionrelated to SmoothnessAlthough0.60section
Indicator functionrelated to SmoothnessFor0.60section

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