Unary operation

In mathematics, an 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.

Examples

Absolute Value

The operation absolute value is a unary operation. The absolute value of a number is its distance from zero.

| 3 | = 3

| -3 | = 3

| 0 | = 0

Opposite of

We find the opposite of a single number.

- (3) = - 3

- ( -3) = 3

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 , , 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.

JavaScript

In JavaScript, these operators are unary:[3]

C family of languages

In the C family of languages, the following operators are unary:[4][5]

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

References
  1. Weisstein, Eric W. "Unary Operation". mathworld.wolfram.com. Retrieved 2020-07-29.
  2. Weisstein, Eric W. "Binary Operation". mathworld.wolfram.com. Retrieved 2020-07-29.
  3. "Unary Operators".
  4. "Chapter 5. Expressions and Operators". C/C++ Language Reference. www-01.ibm.com. Version 6.0. p. 109. Archived from the original on 2012-10-16.
  5. "Unary Operators - C Tutorials - Sanfoundry". www.sanfoundry.com.
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