mathematics

Unary operation

Unary operation is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Unary operation rather than just read about it. In short: 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.

Key takeaways

Unary operation belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Unary operation to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Unary operation from memory before moving on to harder problems.

Reference excerpt

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 ⁠ f : A → A {\displaystyle f:A\rightarrow A} ⁠, where A is a set; the function ⁠ f {\displaystyle f} ⁠ is a unary operation on A. Common notations are prefix notation (e.g. negation ¬, additive inverse −), 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 Obtaining the absolute value of a number is a unary operation. This function is defined as | n | = { n , if n ≥ 0 − n , if n < 0 {\displaystyle |n|={\begin{cases}n,&{\mbox{if }}n\geq 0\\-n,&{\mbox{if }}n<0\end{cases}}} where | n | {\displaystyle |n|} is the absolute value of n {\displaystyle n} .

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

− ( 3 ) = − 3 {\displaystyle -(3)=-3}

− ( − 3 ) = 3 {\displaystyle -(-3)=3}

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 sin {\displaystyle \sin } , cos {\displaystyle \cos } , and tan {\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 Below is a table summarizing common unary operators along with their symbols, description, and examples:

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)

References

External links Media related to Unary operations at Wikimedia Commons

Worked examples

Example 1 — a first encounter with Unary operation

Start with the simplest possible case. Write down what Unary operation claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Unary operation before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Unary operation ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Unary operation

In research: Unary operation appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Unary operation in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Unary operation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Elementary algebra, Operators (programming), Unary operations, so understanding it makes those chapters shorter.
In everyday life: Look for Unary operation outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Unary operation” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Unary operation in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Unary operation means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Unary operation out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Unary operation in simple terms?

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.

Why does Unary operation matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Unary operation?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Unary operation.