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.
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Unary and Binary Operations
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Relational Algebra Operations - Unary
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Mathematics in the Modern World 2 - Use of Numbers and Unary and Binary Operations
Transcription
Examples
Absolute value
Obtaining the absolute value of a number is a unary operation. This function is defined as [3] 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
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/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:
${#x}
PowerShell
- Increment:
++$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
- 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.
- ^ "Absolute value".
- ^ "Unary Operators".
- ^ "Chapter 5. Expressions and Operators". C/C++ Language Reference. Version 6.0. p. 109. Archived from the original on 2012-10-16.
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ignored (help) - ^ "Unary Operators - C Tutorials - Sanfoundry". www.sanfoundry.com.