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In mathematics, a unary operation is an operation with only one operand, i.e. a single input.[1] This is in contrast to binary operations, which use two operands.[2] An example is the function f : A → A, where A is a set. The function f is a unary operation on A.

Common notations are prefix notation (e.g. +, −, ¬), postfix notation (e.g. factorial n!), functional notation (e.g. sin x or sin(x)), and superscripts (e.g. transpose AT). Other notations exist as well. For example, in the case of the square root, a horizontal bar extending the square root sign over the argument can indicate the extent of the argument.

Unary negative and positive

As unary operations have only one operand they are evaluated before other operations containing them. Here is an example using negation:

3 − −2

Here, the first '−' represents the binary subtraction operation, while the second '−' represents the unary negation of the 2 (or '−2' could be taken to mean the integer −2). Therefore, the expression is equal to:

3 − (−2) = 5

Technically there is also a unary positive but it is not needed since we assume a value to be positive:

(+2) = 2

Unary positive does not change the sign of a negative operation:

(+(−2)) = (−2)

In this case a unary negative is needed to change the sign:

(−(−2)) = (+2)


In trigonometry, the trigonometric functions, such as sin {\displaystyle \sin } \sin , cos {\displaystyle \cos } \cos, and tan {\displaystyle \tan } \tan , are unary operations. This is because it is possible to provide only one term as input for these functions and retrieve a result. By contrast, binary operations, such as addition, require two different terms to compute a result.

Examples from programming languages

In Javascript, these operators are unary:[3]

Increment: ++x, x++
Decrement: −−x, x−−
Positive: +x
Negative: −x
Ones' complement: ~x
Logical negation: !x

C family of languages

In the C family of languages, the following operators are unary:[4][5]

Increment: ++x, x++
Decrement: −−x, x−−
Address: &x
Indirection: *x
Positive: +x
Negative: −x
Ones' complement: ~x
Logical negation: !x
Sizeof: sizeof x, sizeof(type-name)
Cast: (type-name) cast-expression

Unix Shell (Bash)

In the Unix/Linux shell (bash/sh), '$' is a unary operator when used for parameter expansion, replacing the name of a variable by its (sometimes modified) value. For example:

Simple expansion: $x
Complex expansion: ${#x}

Windows PowerShell

Increment: ++$x, $x++
Decrement: −−$x, $x−−
Positive: +$x
Negative: −$x
Logical negation: !$x
Invoke in current scope: .$x
Invoke in new scope: &$x
Cast: [type-name] cast-expression
Cast: +$x
Array: ,$array

See also

Binary operation
Iterated binary operation
Ternary operation
Operation (mathematics)
Operator (programming)


Weisstein, Eric W. "Unary Operation". mathworld.wolfram.com. Retrieved 2020-07-29.
Weisstein, Eric W. "Binary Operation". mathworld.wolfram.com. Retrieved 2020-07-29.
"Unary Operators".
"Chapter 5. Expressions and Operators". C/C++ Language Reference. www-01.ibm.com. Version 6.0. p. 109. Archived from the original on 2012-10-16.
"Unary Operators - C Tutorials - Sanfoundry". www.sanfoundry.com.

Undergraduate Texts in Mathematics

Graduate Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia



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