unary

Unary describes a relation or operation involving a single operand. The term comes from the Latin unus meaning “one.” In mathematics, logic, and computer science, unary is used to distinguish things that act on one input from those with two inputs (binary) or more.

In mathematics, a unary operation maps a single element to another. Examples include negation, which sends x to -x, and the identity function, which leaves x unchanged. The unary minus is used to indicate additive inverses, while other one-argument functions such as absolute value or certain trigonometric values are also unary in function, though they may be composed with other operations. In theory, a unary function is one with arity 1.

The unary numeral system, or base-1 representation, expresses a number by a count of a single symbol, usually a tally mark or repeated ones. It is non-positional and impractical for everyday arithmetic, but it serves as a simple model in theoretical computer science and combinatorics.

In computing, a unary operator applies to exactly one operand. Common examples include unary plus and unary minus, which indicate sign; logical negation, denoted by not or !; and bitwise negation, often written ~. Many languages also implement unary increment and decrement operators (such as ++ and --) that modify a single operand. These operators illustrate the concept of arity in programming language design.

In logic and theoretical computer science, a unary predicate or unary function has arity one, meaning it takes a single argument. In linguistics and computer science, unary branching or unary structures describe constructions with a single immediate constituent.

Overall, unary emphasizes the single-input nature of a function, operation, or relation across disciplines.

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