Unary function

A unary function is a function that takes one argument. A unary operator belongs to a subset of unary functions, in that its range coincides with its domain. In contrast, a unary function's domain may or may not coincide with its range.

## Examples

The successor function, denoted [math]\displaystyle{ \operatorname{succ} }[/math], is a unary operator. Its domain and codomain are the natural numbers, its definition is as follows:

[math]\displaystyle{ \begin{align} \operatorname{succ} : \quad & \mathbb{N} \rightarrow \mathbb{N} \\\ & n \mapsto (n + 1) \end{align} }[/math]

In many programming languages such as C, executing this operation is denoted by postfixing [math]\displaystyle{ \mathrel{+{+}} }[/math] to the operand, i.e. the use of [math]\displaystyle{ n\mathrel{+{+}} }[/math] is equivalent to executing the assignment [math]\displaystyle{ n:= \operatorname{succ}(n) }[/math].

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

## See also

* Arity
* Binary function
* Binary operator
* List of mathematical functions
* Ternary operation
* Unary operation

## References

* Foundations of Genetic Programming

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