Binaariset

Binaariset is a term used in some Dutch-language technical literature to denote a set whose elements are binary values or binary strings. In English-language contexts, the idea is usually described as a binary set or as a language over the binary alphabet {0,1}. The term does not correspond to a single formal object, but rather to a broad idea used across computer science and mathematics.

A binaariset can be any subset of {0,1}^*, the set of all finite binary strings, or of {0,1}^n, the set of binary strings of fixed length n. The full set {0,1}^* forms a free monoid under string concatenation; finite subsets are finite binaari sets. Examples include {0,1}, {00,01,10,11}, or {0101,1100}.

Operations on binaarisets typically involve standard set operations or string operations. Union and intersection combine sets; concatenation combines strings to form longer ones; in language terminology, the Kleene star allows building new binary languages from existing ones. Depending on how the set is defined, a binaariset may be prefix-free, regular, or context-free.

Applications of binaarisets appear in digital electronics, data encoding and decoding, coding theory, and automata theory. They underpin representations of information as sequences of bits, as well as the design of finite-state machines and error-detecting codes.

See also: binary alphabet, formal language, regular language, bitset. Note that binaariset is a term encountered in certain Dutch-language texts; in English, the standard phrasing would refer to a binary set or a language over {0,1}.