Unary operation
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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 any function , where A is a set. The function 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.
Examples
Absolute value
Obtaining the absolute value of a number is a unary operation. This function is defined as where is the absolute value of .
Negation
This is used to find the negative value of a single number. Here are some examples:
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 an unary operation extension of factorial.
Trigonometry
In trigonometry, the trigonometric functions, such as , , and , 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
- Binary operation
- Iterated binary operation
- Ternary operation
- Arity
- Operation (mathematics)
- Operator (programming)
References
- ^ 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 in Programming". GeeksforGeeks. 20 March 2024. Retrieved 24 April 2024.
- ^ "Unary Operators".
- ^ "5. Expressions and Operators". C/C++ Language Reference. Version 6.0. p. 109. Archived from the original on 2012-10-16.
- ^ "Unary Operators - C Tutorials - Sanfoundry". www.sanfoundry.com.
- ^ "Shell Arithmetic (Bash Reference Manual)". www.gnu.org. GNU Operating System. Retrieved 24 April 2024.
- ^ Miran, Mohammad Shah (26 October 2023). "Unary Operators in Bash". LinuxSimply. Retrieved 24 April 2024.
- ^ "Expressions - PowerShell". learn.microsoft.com. Microsoft. 3 September 2021. Retrieved 23 April 2024.
External links
Media related to Unary operations at Wikimedia Commons