Unary operation

Short description: Mathematical operation with only one operand

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 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.

## Contents

* 1 Examples
* 1.1 Absolute value
* 1.2 Negation
* 1.3 Factorial
* 1.4 Trigonometry
* 1.5 Examples from programming languages
* 1.5.1 JavaScript
* 1.5.2 C family of languages
* 1.5.3 Unix shell (Bash)
* 1.5.4 PowerShell
* 2 See also
* 3 References
* 4 External links

## Examples

### Absolute value

Obtaining the absolute value of a number is a unary operation. This function is defined as |n|={n,if n≥0−n,if n<0 where |n| is the absolute value of n.

### Negation

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

−(3)=−3

−(−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 sin, cos, and 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)

## References

1. ↑ Weisstein, Eric W.. "Unary Operation" (in en). https://mathworld.wolfram.com/UnaryOperation.html.
2. ↑ Weisstein, Eric W.. "Binary Operation" (in en). https://mathworld.wolfram.com/BinaryOperation.html.
3. ↑ "Unary Operators in Programming". 20 March 2024. https://www.geeksforgeeks.org/unary-operators-in-programming/.
4. ↑ "Unary Operators". https://www.javascripttutorial.net/javascript-unary-operators/.
5. ↑ "5. Expressions and Operators". C/C++ Language Reference. p. 109. http://www-01.ibm.com/support/docview.wss?uid=swg27002103&aid=1.
6. ↑ "Unary Operators - C Tutorials - Sanfoundry". 2 March 2014. http://www.sanfoundry.com/c-tutorials-different-unary-operators-operate-operands/.
7. ↑ "Shell Arithmetic (Bash Reference Manual)". GNU Operating System. https://www.gnu.org/software/bash/manual/html_node/Shell-Arithmetic.html.
8. ↑ Miran, Mohammad Shah (26 October 2023). "Unary Operators in Bash". https://linuxsimply.com/bash-scripting-tutorial/operator/unary-operators/.
9. ↑ "Expressions - PowerShell" (in en-us). Microsoft. 3 September 2021. https://learn.microsoft.com/en-us/powershell/scripting/lang-spec/chapter-07.

## External links

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