View source for Property (mathematics)

In [[Mathematics|mathematics]], a '''property''' is any characteristic that applies to a given [[Set (mathematics)|set]].<ref>{{cite web |url=https://www.mathsisfun.com/sets/sets-introduction.html |title=Introduction to Sets |website=www.mathsisfun.com |access-date=October 15, 2018}}</ref> [[Rigour|Rigorously]], a property ''p'' defined for all elements of a set ''X'' is usually defined as a function ''p'': ''X'' →  {true, false}, that is true whenever the property holds; or, equivalently, as the [[Subset|subset]] of ''X'' for which ''p'' holds; i.e. the set {''x''&nbsp;|&nbsp;''p''(''x'')&nbsp;=&nbsp;true}; ''p'' is its [[Indicator function|indicator function]]. However, it may be objected that the rigorous definition defines merely the [[Extension (semantics)|extension]] of a property, and says nothing about what causes the property to hold for exactly those values. {{Citation needed|date=June 2023}}

== Examples ==

Of [[Philosophy:Mathematical object|objects]]:

* [[Parity (mathematics)|Parity]] is the property of an [[Integer|integer]] of whether it is even or odd

Of [[Operation (mathematics)|operations]]:

* [[Associative property|associative property]]
* [[Commutative property|commutative property]] of [[Binary operation|binary operations]] between [[Real number|real]] and [[Complex number|complex number]]s
* [[Distributive property|distributive property]]

== See also ==
* Unary relation

==References==
{{reflist}}

[[Category:Mathematical terminology]]
[[Category:Mathematical relations]]



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