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 the 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 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[]

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 positive but it is not needed since we assume a value to be positive:

(+2) = 2

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

(+(−2)) = (−2)

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

(−(−2)) = (+2)

Trigonometry[]

In trigonometry, the trigonometric functions, such as ${\displaystyle \sin }$, ${\displaystyle \cos }$, and ${\displaystyle \tan }$, are 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:^[3]

• 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:^[4][5]

• 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}

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[]

External links[]

• Media related to Unary operations at Wikimedia Commons