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Empty set

In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the…

Properties, In other areas of mathematics & Existence

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Overview

Notation

Properties

In other areas of mathematics

Existence

Advanced semantic analysis

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Map overview Semantic statistics

Empty set

Nodes84
Edges83
Triples56
Avg. degree1.98
Density0.02381
Components1

How this topic connects Entity context

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Empty set

Top relations

related to Notation · 13
Empty set → André Weil, Bourbaki, CAPITAL LETTER, Common, Danish, HTML, In, It, LaTeX, Norwegian, The, Unicode, WITH STROKE
related to Axiomatic set theory · 5
Empty set → Even, However, In Zermelo, Now, Standard
related to Category theory · 5
Empty set → As, If, In, The, This
related to Extended real numbers · 5
Empty set → By, For, Since, That, When
related to Set theory · 5
Empty set → In, Neumann, Peano, The, Thus
is a · 4
Empty set → empty set itself, only set with either of these properties.For any set A, standard and widely accepted mathematical concept, unique initial object of the category of sets and functions.The empty set can be turned into a topological space
related to Philosophical issues · 4
Empty set → Darling, The, This, While
related to External links · 3
Empty set → Eric, MathWorld, Weisstein
related to Operations on the empty set · 3
Empty set → Similarly, The, When
related to Properties · 3
Empty set → As, In, The

Important terminology Word statistics

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Important terminology

set empty displaystyle varnothing zero element one elements sets theory every subset numbers existence used considered axiom mathematics two exists

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Empty setis aempty set itself0.90text
Empty setis aonly set with either of these properties.For any set A0.90text
Empty setis aunique initial object of the category of sets and functions.The empty set can be turned into a topological space0.90text
Empty setis astandard and widely accepted mathematical concept0.90text
Danishinstance ofemptyset.When writing in languages0.80text
Norwegianinstance ofemptyset.When writing in languages0.80text
where the empty set character may be confused with the alphabetic letter Øinstance ofemptyset.When writing in languages0.80text
Empty setrelated to Axiomatic set theoryIn Zermelo0.60section
Empty setrelated to Axiomatic set theoryHowever0.60section
Empty setrelated to Axiomatic set theoryStandard0.60section
Empty setrelated to Axiomatic set theoryNow0.60section
Empty setrelated to Axiomatic set theoryEven0.60section

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    Min side: 3
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