unäre

Unäre, or unary in English, is an adjective used to describe a relation, operation, or function that takes exactly one input or operand. The term derives from Latin unus, meaning one, and is used across mathematics, logic, and computer science to distinguish single-argument processes from binary, ternary, or higher-arity operations.

In mathematics, a unary operation or function maps a set to itself or to another set, using a single argument. Common examples include negation x ↦ −x on the real numbers, absolute value x ↦ |x|, and the reciprocal x ↦ 1/x (where defined). The factorial function n ↦ n! is unary on the natural numbers, as it consumes one input to produce another value. In set theory, the complement operation is unary on the power set of a universal set: A ↦ A^c, the set of all elements not in A.

In logic and computer science, unary operators and predicates are widespread. Logical negation ¬P acts on a single proposition. In programming languages, unary operators include unary plus and minus, logical NOT, bitwise NOT, and dereference or address operators. Some languages also feature unary increment and decrement operators, which modify a single operand.

Terminology around unary operations emphasizes arity, or the number of operands an operation uses. Unary, monadic, or one-place are commonly used terms to describe 1-ary operations, as opposed to binary (two-argument) and higher-arity operations.

See also: arity, unary operator, unary predicate, monadic.