Unary operation


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 : AA, 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. sinx 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 edit

Absolute value edit

Obtaining the absolute value of a number is a unary operation. This function is defined as   where   is the absolute value of  .

Negation edit

This is used to find the negative value of a single number. Here are some examples:


Factorial edit

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 edit

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 edit

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 edit

In JavaScript, these operators are unary:[4]

C family of languages edit

In the C family of languages, the following operators are unary:[5][6]

Unix shell (Bash) edit

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 edit

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 edit

References edit

  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 in Programming". GeeksforGeeks. 20 March 2024. Retrieved 24 April 2024.
  4. ^ "Unary Operators".
  5. ^ "5. Expressions and Operators". C/C++ Language Reference. Version 6.0. p. 109. Archived from the original on 2012-10-16.
  6. ^ "Unary Operators - C Tutorials - Sanfoundry". www.sanfoundry.com.
  7. ^ "Shell Arithmetic (Bash Reference Manual)". www.gnu.org. GNU Operating System. Retrieved 24 April 2024.
  8. ^ Miran, Mohammad Shah (26 October 2023). "Unary Operators in Bash". LinuxSimply. Retrieved 24 April 2024.
  9. ^ "Expressions - PowerShell". learn.microsoft.com. Microsoft. 3 September 2021. Retrieved 23 April 2024.

External links edit

  •   Media related to Unary operations at Wikimedia Commons