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 \( \operatorname{succ} \), 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.
See also
Arity
Binary function
Binary operator
List of mathematical functions
Ternary operation
Unary operation
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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