Table of Contents
53 relations: Abelian group, Abstract algebra, Algebraic structure, Arity, Associative property, Axiom, Bijection, Binary operation, Boolean algebra, Boolean algebra (structure), Boolean domain, Boolean function, Bounded set, Canonical normal form, Commutative property, Concatenation, De Morgan's laws, Decidability (logic), Decision problem, Distributive lattice, Distributive property, Duality (order theory), Elementary algebra, Exponential function, First-order logic, G. Spencer-Brown, Lattice (order), Laws of Form, Logical conjunction, Logical disjunction, Logical equivalence, Logical NOR, Map (mathematics), Mathematics, Metatheorem, Negation, Operation (mathematics), Order of operations, Order theory, Partially ordered set, Paul Halmos, Polynomial, Principle of bivalence, Quantifier elimination, Semiring, Sheffer stroke, Stanford Encyclopedia of Philosophy, Syntax, Theory (mathematical logic), Unary operation, ... Expand index (3 more) »
Abelian group
In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
See Two-element Boolean algebra and Abelian group
Abstract algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements.
See Two-element Boolean algebra and Abstract algebra
Algebraic structure
In mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy.
See Two-element Boolean algebra and Algebraic structure
Arity
In logic, mathematics, and computer science, arity is the number of arguments or operands taken by a function, operation or relation.
See Two-element Boolean algebra and Arity
Associative property
In mathematics, the associative property is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result. Two-element Boolean algebra and associative property are Elementary algebra.
See Two-element Boolean algebra and Associative property
Axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
See Two-element Boolean algebra and Axiom
Bijection
A bijection, bijective function, or one-to-one correspondence between two mathematical sets is a function such that each element of the first set (the domain) is mapped to exactly one element of the second set (the codomain).
See Two-element Boolean algebra and Bijection
Binary operation
In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element.
See Two-element Boolean algebra and Binary operation
Boolean algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra.
See Two-element Boolean algebra and Boolean algebra
Boolean algebra (structure)
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. Two-element Boolean algebra and Boolean algebra (structure) are Boolean algebra.
See Two-element Boolean algebra and Boolean algebra (structure)
Boolean domain
In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true. Two-element Boolean algebra and Boolean domain are Boolean algebra.
See Two-element Boolean algebra and Boolean domain
Boolean function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually, or). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Two-element Boolean algebra and Boolean function are Boolean algebra.
See Two-element Boolean algebra and Boolean function
Bounded set
In mathematical analysis and related areas of mathematics, a set is called bounded if all of its points are within a certain distance of each other.
See Two-element Boolean algebra and Bounded set
Canonical normal form
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form (CDNF), minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. Two-element Boolean algebra and canonical normal form are Boolean algebra.
See Two-element Boolean algebra and Canonical normal form
Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. Two-element Boolean algebra and commutative property are Elementary algebra.
See Two-element Boolean algebra and Commutative property
Concatenation
In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end.
See Two-element Boolean algebra and Concatenation
De Morgan's laws
In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. Two-element Boolean algebra and De Morgan's laws are Boolean algebra.
See Two-element Boolean algebra and De Morgan's laws
Decidability (logic)
In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer.
See Two-element Boolean algebra and Decidability (logic)
Decision problem
In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values.
See Two-element Boolean algebra and Decision problem
Distributive lattice
In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other.
See Two-element Boolean algebra and Distributive lattice
Distributive property
In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality x \cdot (y + z). Two-element Boolean algebra and distributive property are Elementary algebra.
See Two-element Boolean algebra and Distributive property
Duality (order theory)
In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop or Pd.
See Two-element Boolean algebra and Duality (order theory)
Elementary algebra
Elementary algebra, also known as college algebra, encompasses the basic concepts of algebra.
See Two-element Boolean algebra and Elementary algebra
Exponential function
The exponential function is a mathematical function denoted by f(x).
See Two-element Boolean algebra and Exponential function
First-order logic
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
See Two-element Boolean algebra and First-order logic
G. Spencer-Brown
George Spencer-Brown (2 April 1923 – 25 August 2016) was an English polymath best known as the author of Laws of Form.
See Two-element Boolean algebra and G. Spencer-Brown
Lattice (order)
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.
See Two-element Boolean algebra and Lattice (order)
Laws of Form
Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. Two-element Boolean algebra and Laws of Form are Boolean algebra.
See Two-element Boolean algebra and Laws of Form
Logical conjunction
In logic, mathematics and linguistics, and (\wedge) is the truth-functional operator of conjunction or logical conjunction.
See Two-element Boolean algebra and Logical conjunction
Logical disjunction
In logic, disjunction, also known as logical disjunction or logical or or logical addition or inclusive disjunction, is a logical connective typically notated as \lor and read aloud as "or".
See Two-element Boolean algebra and Logical disjunction
Logical equivalence
In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model.
See Two-element Boolean algebra and Logical equivalence
Logical NOR
In Boolean logic, logical NOR, non-disjunction, or joint denial is a truth-functional operator which produces a result that is the negation of logical or.
See Two-element Boolean algebra and Logical NOR
Map (mathematics)
In mathematics, a map or mapping is a function in its general sense.
See Two-element Boolean algebra and Map (mathematics)
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
See Two-element Boolean algebra and Mathematics
Metatheorem
In logic, a metatheorem is a statement about a formal system proven in a metalanguage.
See Two-element Boolean algebra and Metatheorem
Negation
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P to another proposition "not P", standing for "P is not true", written \neg P, \mathord P or \overline.
See Two-element Boolean algebra and Negation
Operation (mathematics)
In mathematics, an operation is a function which takes zero or more input values (also called "operands" or "arguments") to a well-defined output value.
See Two-element Boolean algebra and Operation (mathematics)
Order of operations
In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression.
See Two-element Boolean algebra and Order of operations
Order theory
Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations.
See Two-element Boolean algebra and Order theory
Partially ordered set
In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other.
See Two-element Boolean algebra and Partially ordered set
Paul Halmos
Paul Richard Halmos (Halmos Pál; 3 March 3 1916 – 2 October 2006) was a Hungarian-born American mathematician and statistician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces).
See Two-element Boolean algebra and Paul Halmos
Polynomial
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.
See Two-element Boolean algebra and Polynomial
Principle of bivalence
In logic, the semantic principle (or law) of bivalence states that every declarative sentence expressing a proposition (of a theory under inspection) has exactly one truth value, either true or false.
See Two-element Boolean algebra and Principle of bivalence
Quantifier elimination
Quantifier elimination is a concept of simplification used in mathematical logic, model theory, and theoretical computer science.
See Two-element Boolean algebra and Quantifier elimination
Semiring
In abstract algebra, a semiring is an algebraic structure.
See Two-element Boolean algebra and Semiring
Sheffer stroke
In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both".
See Two-element Boolean algebra and Sheffer stroke
Stanford Encyclopedia of Philosophy
The Stanford Encyclopedia of Philosophy (SEP) is a freely available online philosophy resource published and maintained by Stanford University, encompassing both an online encyclopedia of philosophy and peer-reviewed original publication.
See Two-element Boolean algebra and Stanford Encyclopedia of Philosophy
Syntax
In linguistics, syntax is the study of how words and morphemes combine to form larger units such as phrases and sentences.
See Two-element Boolean algebra and Syntax
Theory (mathematical logic)
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language.
See Two-element Boolean algebra and Theory (mathematical logic)
Unary operation
In mathematics, a unary operation is an operation with only one operand, i.e. a single input. Two-element Boolean algebra and unary operation are Elementary algebra.
See Two-element Boolean algebra and Unary operation
Universal algebra
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures.
See Two-element Boolean algebra and Universal algebra
Universe (mathematics)
In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains all the entities one wishes to consider in a given situation.
See Two-element Boolean algebra and Universe (mathematics)
Willard Van Orman Quine
Willard Van Orman Quine (known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century".
See Two-element Boolean algebra and Willard Van Orman Quine
References
Also known as 2 (algebra), Boolean arithmetic, Two element boolean algebra.