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 [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 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 [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
• Ternary operation
• Unary operation

References

• Foundations of Genetic Programming

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