Unary operation

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 any function ⁠${\displaystyle f:A\rightarrow A}$⁠, where A is a set; the function ⁠${\displaystyle f}$⁠ 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 A^T). 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.

Examples

Absolute value

Obtaining the absolute value of a number is a unary operation. This function is defined as ${\displaystyle |n|={\begin{cases}n,&{\mbox{if }}n\geq 0\\-n,&{\mbox{if }}n<0\end{cases}}}$ where ${\displaystyle |n|}$ is the absolute value of ${\displaystyle n}$.

Negation

Negation is used to find the negative value of a single number. Here are some examples:

${\displaystyle -(3)=-3}$

${\displaystyle -(-3)=3}$

Factorial

For any positive integer n, the product of the integers less than or equal to n is a unary operation called factorial. In the context of complex numbers, the gamma function is a unary operation extension of factorial.

Trigonometry

In trigonometry, the trigonometric functions, such as ${\displaystyle \sin }$, ${\displaystyle \cos }$, and ${\displaystyle \tan }$, can be seen as 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

Below is a table summarizing common unary operators along with their symbols, description, and examples:^[3]

Operator	Symbol	Description	Example
Increment	++	Increases the value of a variable by 1	x = 2; ++x; // x is now 3
Decrement	−-	Decreases the value of a variable by 1	y = 10; --y; // y is now 9
Unary Plus	+	Indicates a positive value	a = -5; b = +a; // b is -5
Unary Minus	-	Indicates a negative value	c = 4; d = -c; // d is -4
Logical NOT	!	Negates the truth value of a Boolean expression	flag = true; result = !flag; // result is false
Bitwise NOT	~	Bitwise negation, flips the bits of an integer	num = 5; result = ~num; // result is -6

JavaScript

In JavaScript, these operators are unary:^[4]

• 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:^[5][6]

• 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 shell (Bash/Bourne Shell), e.g., the following operators are unary:^[7][8]

• Pre and Post-Increment: ++$x, $x++
• Pre and Post-Decrement: --$x, $x--
• Positive: +$x
• Negative: -$x
• Logical negation: !$x
• Simple expansion: $x
• Complex expansion: ${#x}

PowerShell

In the PowerShell, the following operators are unary:^[9]

• 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

• Unary function
• Binary operation
• Iterated binary operation
• Binary function
• Ternary operation
• Arity
• Operation (mathematics)
• Operator (programming)