Editing Arity (section)

== Terminology ==
[[Latin]]ate names are commonly used for specific arities, primarily based on Latin [[distributive number]]s meaning "in group of ''n''", though some are based on Latin [[cardinal number]]s or [[ordinal number]]s. For example, 1-ary is based on cardinal ''unus'', rather than from distributive ''singulī'' that would result in ''singulary''. 

{| class="wikitable"
|-
! ''n''-ary !! Arity (Latin based) !! Adicity (Greek based) !! Example in mathematics !! Example in computer science
|-
| 0-ary || nullary (from ''nūllus'') || niladic || a [[constant (mathematics)|constant]]  || a function without arguments, [[Truth|True]], [[Falsity|False]]
|-
| 1-ary || [[Unary operation|unary]] || monadic || [[additive inverse]] || logical [[Logical NOT|NOT]] operator
|-
| 2-ary || [[Binary operation|binary]] || dyadic || [[addition]] || logical [[Logical OR|OR]], [[Exclusive or|XOR]], [[Logical AND|AND]] operators
|-
| 3-ary || [[Ternary operation|ternary]] || triadic || [[Triple product|triple product of vectors]] || [[ternary conditional operator]]
|-
| 4-ary || quaternary || tetradic ||  ||
|-
| 5-ary || quinary  || pentadic ||  ||
|-
| 6-ary || senary || hexadic ||  || 
|-
| 7-ary || septenary || hebdomadic ||  || 
|-
| 8-ary || octonary || ogdoadic ||  || 
|-
| 9-ary || novenary (alt. nonary) || enneadic ||  || 
|-
| 10-ary || denary (alt. decenary) || decadic ||  || 
|-
| more than 2-ary || multary and multiary || polyadic ||  || 
|-
| varying || || variadic || sum; e.g., Σ || [[variadic function]], [[Reduce (parallel pattern)|reduce]]
|}

''n''-''ary'' means having ''n'' operands (or parameters), but is often used as a synonym of "polyadic".

These words are often used to describe anything related to that number (e.g., undenary chess is a [[chess variant]] with an 11×11 board, or the [[Millenary Petition]] of 1603).

The arity of a [[relation (mathematics)|relation]] (or [[predicate (mathematical logic)|predicate]]) is the dimension of the [[domain of a function|domain]] in the corresponding [[Cartesian product]]. (A function of arity ''n'' thus has arity ''n''+1 considered as a relation.) 

In [[computer programming]], there is often a [[Syntax (programming languages)|syntactical]] distinction between [[Operator (programming)|operators]] and [[Function (computer science)|functions]]; syntactical operators usually have arity 1, 2, or 3 (the [[Ternary operation|ternary operator]] [[?:]] is also common).  Functions vary widely in the number of arguments, though large numbers can become unwieldy. Some programming languages also offer support for [[variadic functions]], i.e., functions syntactically accepting a variable number of arguments.