Unary function

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

Examples

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

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

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

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.