In mathematics, a 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. negation , additive inverse ), 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
Absolute value Obtaining the absolute value of a number is a unary operation. This function is defined as where is the absolute value of .
Negation Negation 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 a 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 Below is a table summarizing common unary operators along with their symbols, description, and examples:
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 In JavaScript, these operators are unary: Increment: ++x, x++ Decrement: --x, x-- Positive: +x Negative: -x Ones' complement: ~x Logical negation: !x
Python In Python, there are no increment or decrement operators, but the following unary operators are available: Positive: +x Negative: -x Ones' complement: ~x Logical negation: not 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 shell (Bash/Bourne Shell), e.g., the following operators are unary: Pre and Post-Increment: ++$x, $x++ Pre and Post-Decrement: --$x, $x-- Positive: +$x Negative: -$x Logical negation: !$x Simple expansion: $x Complex expansion: ${#x}
PowerShell In the PowerShell, the following operators are unary: Increment: ++$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 Unary function Binary operation Iterated binary operation Binary function Ternary operation Arity Operation (mathematics) Operator (programming)
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