Unary function: Difference between revisions

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

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A '''unary function''' is a [[function (mathematics)|function]] that takes one [[Parameter (computer science)|argument]], an [[N-ary function]] with arity 1.

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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 [[codomain]] coincides with its [[___domain of a function|___domain]]. In contrast, a unary function's ___domain need not coincide with its range.

==References Examples ==

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

: <math display="block">

\begin{align}

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

& n \mapsto (n + 1)

\end{align}

</math>

In some [[programming language]]s such as [[C (programming language)|C]], executing this operation is denoted by [[Reverse Polish notation|postfixing]] {{code|++}} to the operand, i.e. the use of {{code|n++}} 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 operation]]

* [[Iterated binary operation]]

* [[Ternary operation]]

* [[Unary operation]]

== Bibliography ==

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

{{Authority control}}

[[Category:Functions and mappings]]

[[Category:Types of functions]]

[[Category:Unary operations|*]]

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