# 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.

## Examples

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

{\displaystyle {\begin{aligned}\operatorname {succ} :\quad &\mathbb {N} \rightarrow \mathbb {N} \\&n\mapsto (n+1)\end{aligned}}}

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

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