View source for Unary function

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

== 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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