mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, a unary operation is an operation with only one

operand In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on. Unknown operands in equalities of expressions can be found by equation solving. Example The following arithmetic expres ...

, i.e. a single input. This is in contrast to ''

binary operation In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, a binary operation ...

s'', which use two operands. An example is any function , where is a

set Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electro ...

; the function is a unary operation on . Common notations are

prefix notation Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation, Eastern Notation or simply prefix notation, is a mathematical notation in which operators ''precede'' their oper ...

(e.g. ¬, −),

postfix notation Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which Operation (mathematics), operators ''follow'' their operands, in contrast to pr ...

(e.g.

factorial In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times ...

), functional notation (e.g. or ), and

superscript A subscript or superscript is a character (such as a number or letter) that is set slightly below or above the normal line of type, respectively. It is usually smaller than the rest of the text. Subscripts appear at or below the baseline, wh ...

s (e.g.

transpose In linear algebra, the transpose of a Matrix (mathematics), matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix by producing another matrix, often denoted by (among other ...

). Other notations exist as well, for example, in the case of the

square root In mathematics, a square root of a number is a number such that y^2 = x; in other words, a number whose ''square'' (the result of multiplying the number by itself, or y \cdot y) is . For example, 4 and −4 are square roots of 16 because 4 ...

, 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 In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if x is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), ...

of a number is a unary operation. This function is defined as

, n,  = \begin n, & \mbox n\geq0 \\ -n, & \mbox n<0 \end

where

, n,

is the absolute value of

n

Negation

Negation In logic, negation, also called the logical not or logical complement, is an operation (mathematics), operation that takes a Proposition (mathematics), proposition P to another proposition "not P", written \neg P, \mathord P, P^\prime or \over ...

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

-(3) = -3

-( -3) = 3

Factorial

For any positive integer ''n'', the product of the integers less than or equal to ''n'' is a unary operation called

. In the context of

complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...

s, the

gamma function In mathematics, the gamma function (represented by Γ, capital Greek alphabet, Greek letter gamma) is the most common extension of the factorial function to complex numbers. Derived by Daniel Bernoulli, the gamma function \Gamma(z) is defined ...

is a unary operation extension of factorial.

Trigonometry

trigonometry Trigonometry () is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The fiel ...

, the

trigonometric functions In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all ...

, 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 Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol, +) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication, and Division (mathematics), divis ...

, 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:

JavaScript

JavaScript JavaScript (), often abbreviated as JS, is a programming language and core technology of the World Wide Web, alongside HTML and CSS. Ninety-nine percent of websites use JavaScript on the client side for webpage behavior. Web browsers have ...

, these operators are unary: *

Increment Increment or incremental may refer to: *Incrementalism, a theory (also used in politics as a synonym for gradualism) * Increment and decrement operators, the operators ++ and -- in computer programming * Incremental computing * Incremental backup ...

: ++x, x++ * Decrement: --x, x-- *Positive: +x *Negative: -x *

Ones' complement The ones' complement of a binary number is the value obtained by inverting (flipping) all the bits in the Binary number, binary representation of the number. The name "ones' complement" refers to the fact that such an inverted value, if added t ...

: ~x *

Logical negation In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P, \mathord P, P^\prime or \overline. It is interpreted intuitively as being true ...

: !x

C family of languages

In the C family of languages, the following operators are unary: *

: ++x, x++ * Decrement: --x, x-- *

Address An address is a collection of information, presented in a mostly fixed format, used to give the location of a building, apartment, or other structure or a plot of land, generally using border, political boundaries and street names as references, ...

: &x * Indirection: *x *Positive: +x *Negative: -x *

: ~x *

: !x *

Sizeof sizeof is a unary operator in the C and C++ programming languages that evaluates to the storage size of an expression or a data type, measured in units sized as char. Consequently, the expression sizeof(char) evaluates to 1. The number of b ...

: sizeof x, sizeof(type-name) *

Cast Cast may refer to: Music * Cast (band), an English alternative rock band * Cast (Mexican band), a progressive Mexican rock band * The Cast, a Scottish musical duo: Mairi Campbell and Dave Francis * ''Cast'', a 2012 album by Trespassers William ...

: (''type-name'') ''cast-expression''

Unix shell (Bash)

In the

Unix shell A Unix shell is a Command-line_interface#Command-line_interpreter, command-line interpreter or shell (computing), shell that provides a command line user interface for Unix-like operating systems. The shell is both an interactive command languag ...

( Bash/

Bourne Shell The Bourne shell (sh) is a shell command-line interpreter for computer operating systems. It first appeared on Version 7 Unix, as its default shell. Unix-like systems continue to have /bin/sh—which will be the Bourne shell, or a symbolic lin ...

), 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: $

PowerShell

In the

PowerShell PowerShell is a shell program developed by Microsoft for task automation and configuration management. As is typical for a shell, it provides a command-line interpreter for interactive use and a script interpreter for automation via a langu ...

, 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

References

External links

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