Einwertig

Einwertig (German for “single‑valued” or “unary”) is an adjective used in several technical fields to describe objects that possess only one value, output, or characteristic at a time. In mathematics a function is called einwertig when each element of its domain is associated with exactly one element of its codomain; this is the standard definition of a function in set‑theoretic terms. The property contrasts with multivalued relations, in which a single argument may correspond to several results.

In logic and computer science the term is applied to operators or predicates that accept a single operand or argument. Unary logical operators such as negation (¬) are einwertig, as they transform one proposition into another. Similarly, unary functions in programming languages take one input parameter and return one output value.

In electrical engineering einwertig is used chiefly in the context of alternating‑current systems. A einwertiges Wechselstromnetz (single‑phase AC system) comprises one sinusoidal voltage waveform, in contrast to dreiphasig (three‑phase) networks that contain three mutually displaced phases. Single‑phase supply is common in residential installations, where it provides adequate power for typical household loads.

The concept also appears in statistics, where a einwertige Variable denotes a variable that can assume only one category or measurement at a time, such as a binary or nominal attribute. In all applications the central idea remains the same: an entity that yields a single, unambiguous result for each input or condition. Related terms include multivalued, polyvalued, and n‑ary, which describe systems with two or more simultaneous values or arguments.