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Arity
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{{Short description|Number of arguments required by a function}} {{redirects here|Adicity|text=Not to be confused with [[Acidity]].}} In [[logic]], [[mathematics]], and [[computer science]], '''arity''' ({{IPAc-en|audio=en-us-arity.ogg|Λ|Γ¦r|α΅»|t|i}}) is the number of [[argument of a function|arguments]] or [[operand]]s taken by a [[function (mathematics)|function]], [[operation (mathematics)|operation]] or [[relation (mathematics)|relation]]. In mathematics, arity may also be called rank,<ref name="Hazewinkel2001">{{cite book|author-link=Michiel Hazewinkel|first=Michiel|last=Hazewinkel|title=Encyclopaedia of Mathematics, Supplement III|url=https://books.google.com/books?id=47YC2h295JUC&pg=PA3|year=2001|publisher=Springer|isbn=978-1-4020-0198-7|page=3}}</ref><ref name="Schechter1997">{{cite book|first=Eric|last=Schechter|title=Handbook of Analysis and Its Foundations|url=https://books.google.com/books?id=eqUv3Bcd56EC&pg=PA356|year=1997|publisher=Academic Press|isbn=978-0-12-622760-4|page=356}}</ref> but this word can have many other meanings. In logic and [[philosophy]], arity may also be called '''adicity''' and '''degree'''.<ref name="DetlefsenBacon1999">{{cite book|first1=Michael |last1=Detlefsen|first2=David Charles|last2=McCarty|first3=John B.|last3=Bacon|title=Logic from A to Z|url=https://archive.org/details/logicfromtoz0000detl|url-access=registration |year=1999|publisher=Routledge|isbn=978-0-415-21375-2|page=[https://archive.org/details/logicfromtoz0000detl/page/7 7]}}</ref><ref name="CocchiarellaFreund2008">{{cite book|first1=Nino B.|last1=Cocchiarella|first2=Max A.|last2=Freund|title=Modal Logic: An Introduction to its Syntax and Semantics|url=https://books.google.com/books?id=zLmxqytfLhgC&pg=PA121|year=2008|publisher=Oxford University Press|isbn=978-0-19-536658-7|page=121}}</ref> In [[linguistics]], it is usually named '''[[valency (linguistics)|valency]]'''.<ref name="Crystal2008">{{cite book|first=David|last=Crystal|title=Dictionary of Linguistics and Phonetics|year=2008|publisher=John Wiley & Sons|isbn=978-1-405-15296-9|page=507|edition=6th}}</ref>
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