Absolute value

Obtaining the absolute value of a number is a unary operation. This function is defined as ${\displaystyle |n|={\begin{cases}n,&{\mbox{if }}n\geq 0\\-n,&{\mbox{if }}n<0\end{cases}}}$^[3] where ${\displaystyle |n|}$ is the absolute value of ${\displaystyle n}$.

Negation

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

${\displaystyle -(3)=-3}$

${\displaystyle -(-3)=3}$

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:

${\displaystyle 3}$${\displaystyle -}$${\displaystyle -}$${\displaystyle 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:

${\displaystyle 3}$${\displaystyle -}$${\displaystyle (-}$${\displaystyle 2)}$${\displaystyle =5}$

Technically, there is also a unary + operation but it is not needed since we assume an unsigned value to be positive:

${\displaystyle +2=2}$

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

${\displaystyle +}$${\displaystyle (-}$${\displaystyle 2)}$${\displaystyle =}$ ${\displaystyle -2}$

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

${\displaystyle -(-2)=+2}$

Trigonometry

In trigonometry, the trigonometric functions, such as ${\displaystyle \sin }$, ${\displaystyle \cos }$, and ${\displaystyle \tan }$, 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, require two different terms to compute a result.

Examples from programming languages