Unary function

Template:Short description Template:Multiple issues 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 $\mathrm{succ}$, is a unary operator. Its domain and codomain are the natural numbers; its definition is as follows:

$$\begin{array}{rl}\mathrm{succ}:& \mathbb{\mathbb{N}}\to \mathbb{\mathbb{N}}\\ & n\mapsto (n+1)\end{array}$$

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 $n:=\mathrm{succ}(n)$.

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.

See also

• Arity
• Binary function
• Binary operation
• Iterated binary operation
• Ternary operation
• Unary operation

Bibliography

• Foundations of Genetic Programming

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