Unary function: Difference between revisions

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{{Short description|Function that takes one argument}}

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In [[mathematics]], a '''unary function''' is a [[function (mathematics)|function]] that takes one [[Arity|argument]]. A [[unary operator]] belongs to a subset of unary functions, in that its [[range of a function|range]] coincides with its [[___domain of a function|___domain]]. In contrast, a unary function's ___domain may or may not coincide with its range.

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In [[mathematics]], a '''unary function''' is a [[function (mathematics)|function]] that takes one [[Arity|argument]]. A [[unary operator]] belongs to a subset of unary functions, in that its [[range of a function|rangecodomain]] coincides with its [[___domain of a function|___domain]]. In contrast, a unary function's ___domain may or mayneed not coincide with its range.

== Examples ==

The [[successor function]], denoted <math>\operatorname{succ}</math>, is a unary operator. Its ___domain and codomain are the [[Naturalnatural number|natural numbers]],s; its definition is as follows:

: <math display="block">

:<math display="block">

\begin{align}

\operatorname{succ} : \quad & \mathbb{N} \rightarrow \mathbb{N} \\

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</math>

In manysome [[Programmingprogramming language|programming languages]]s such as [[C (programming language)|C]], executing this operation is denoted by [[Reverse Polish notation|postfixing]] <math>\mathrel{+{code|++}}</math> to the operand, i.e. the use of <math>n\mathrel{+{code|n++}} </math> is equivalent to executing the assignment <math> n:= \operatorname{succ}(n)</math>.

Many of the [[elementary function]]s are unary functions, including the [[trigonometric functions]], [[logarithm]] with a specified base, [[exponentiation]] to a particular power or base, and [[hyperbolic function]]s.

== See also ==

* [[Arity]]

* [[Binary function]]

* [[Binary operatoroperation]]

* [[Iterated binary operation]]

*[[List of mathematical functions]]

* [[Ternary operation]]

* [[Unary operation]]

==References Bibliography ==

* [http://www.cs.ucl.ac.uk/staff/W.Langdon/FOGP Foundations of Genetic Programming]

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[[Category:Functions and mappings]]

[[Category:Types of functions]]

[[Category:Unary operations|*]]

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