Definition:Operation/Unary Operation

Definition

A unary operation is the special case of an operation where the operation has exactly one operand.

Thus, a unary operation on a set $S$ is a mapping whose domain and codomain are both $S$.

Examples

Square Root

An example of a unary operation from algebra is $\sqrt{}$ (that is, the square root sign).

Self-Map

Let $S$ be a set.

Let $u: S \to S$ be a self-map whose domain and codomain are both $S$.

Then $u$ is an example of a unary operation.

All Mappings are Unary

To a set theorist, all mappings are unary operations.

Also known as

A unary operation is also known as a unary operator.

Also see

• Results about unary operations can be found here.

Linguistic Note

The word unary is pronounced yoo-nary.

Hence when the indefinite article precedes it, the form is (for example) a unary operation.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 18$: Induced $N$-ary Operations
• 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 0.5$
• 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): Chapter $1$: Rings - Definitions and Examples: $1$: The definition of a ring
• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): Appendix $\text{A}.8$: Cartesian Product
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): unary operation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): unary operation
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): operation