unary functional symbol

In mathematics, an unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands. An example is any function , where is a set. The function is a unary operation on .

Common notations are prefix notation (e.g. ¬, −), postfix notation (e.g. factorial ), functional notation (e.g. or ), and superscripts (e.g. transpose ). 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

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 + operation but it is not needed since we assume an unsigned value to be positive:

:+2 = 2

The unary + operation does not change the sign of a negative operation:

:+(−2) = −2

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

:−(−2) = +2

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

JavaScript

In JavaScript, these operators are unary:
*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:

*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: $

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
* Arity
* Operation (mathematics)
* Operator (programming)

References

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External links

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{{DEFAULTSORT:Unary Operation
Elementary algebra
Operators (programming)