Boolean algebra en · NOUN
Etymology
Named after George Boole (1815–1864), an English mathematician, educator, philosopher and logician.
Meanings
-
An algebraic structure (Σ,∨,∧,∼,0,1) where ∨ and ∧ are idempotent binary operators, ∼ is a unary involutory operator (called "complement"), and 0 and 1 are nullary operators (i.e., constants), such that (Σ,∨,0) is a commutative monoid, (Σ,∧,1) is a commutative monoid, ∧ and ∨ distribute with respect to each other, and such that combining two complementary elements through one binary operator yields the identity of the other binary operator. (See Boolean algebra (structure)#Axiomatics.)
The set of divisors of 30, with binary operators: g.c.d. and l.c.m., unary operator: division into 30, and identity elements: 1 and 30, forms a Boolean algebra.
A Boolean algebra is a De Morgan algebra which also satisfies the law of excluded middle and the law of noncontradiction.
- Specifically, an algebra in which all elements can take only one of two values (typically 0 and 1, or "true" and "false") and are subject to operations based on AND, OR and NOT
- The study of such algebras; Boolean logic, classical logic.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| Boolean algebras | Number=Plur | lexicographic |
Deriveds
Hypernyms
Heyting algebra · MV-algebra · distributive lattice · De Morgan algebra · Kleene algebra · Ockham algebra · residuated lattice
Hyponyms
Relateds
Boolean ring · Boolean lattice
Synonyms
switching algebra (Specifically ...)
Translations (20)
mk Булова алге́бра (algebraic structure) · sh Booleova algebra (algebraic structure) · bg Булева алгебра (algebraic structure) · it algebra booleana (algebraic structure) · hu Boole-algebra (algebraic structure) · it reticolo booleano (algebraic structure) · sv Boolesk algebra (algebraic structure) · ja ブール代数 (algebraic structure) · cs booleovská algebra (algebraic structure) · de boolesche Algebra (algebraic structure) · fr algèbre de Boole (algebraic structure) · it algebra di Boole (algebraic structure) · ko 부울 대수 (algebraic structure) · pl algebra Boole'a (algebraic structure) · ko 불 대수 (algebraic structure) · ro algebră booleană (algebraic structure) · fr algèbre booléenne (algebraic structure) · ru бу́лева а́лгебра (algebraic structure) · cmn 布爾代數 /布尔代数 (algebraic structure) · cs Booleova algebra (algebraic structure)