In set theory, the complement of a set A, often denoted by A∁{\displaystyle A^{\complement }} (or A′), is the set of elements not in A. When all elements...

set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures...

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations...

triangle, with ratio −1/2 Complement (set theory) Complementary event in probability Logical complement Bitwise complement Complements in boolean algebra Complementary...

In set theory, the intersection of two sets A{\displaystyle A} and B,{\displaystyle B,} denoted by A∩B,{\displaystyle A\cap B,} is the set containing...

inversion, and complementation. Some theorists apply the methods of musical set theory to the analysis of rhythm as well. Although musical set theory is often...

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any...

is only one empty set. Sets are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard...

Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are...

of sets Boolean function Complement (set theory) Difference (set theory) Exclusive or Fuzzy set Intersection (set theory) Jaccard index List of set identities...

algebra of sets are some of the elementary properties of the algebra of union (infix operator: ∪), intersection (infix operator: ∩), and set complement (postfix...

In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in...

In mathematics, especially in the area of algebra known as group theory, a complement of a subgroup H in a group G is a subgroup K of G such that G=HK={hk:h∈H...

the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique...

Class (set theory) Complement (set theory) Complete Boolean algebra Continuum (set theory) Suslin's problem Continuum hypothesis Countable set Descriptive...

Borel set is Borel, not all analytic sets are Borel sets. A set is coanalytic if its complement is analytic. Many questions in descriptive set theory ultimately...

Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces...

In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains...

"Set Theory", Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University Suppes, Patrick (1972) [1960], Axiomatic Set Theory,...

In computational complexity theory, the complement of a decision problem is the decision problem resulting from reversing the yes and no answers. Equivalently...

In the mathematical field of graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices of...

order theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e...

In measure theory, a conull set is a set whose complement is null, i.e., the measure of the complement is zero. For example, the set of irrational numbers...

In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously...

In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in...

number Codomain Complement (set theory) Constructible universe Continuum hypothesis Countable set Decidable set Denumerable set Disjoint sets Disjoint union...

Class (set theory) Complement (set theory) Complete Boolean algebra Continuum (set theory) Suslin's problem Continuum hypothesis Countable set Descriptive...

functional analysis, the orthogonal complement of a subspace W of a vector space V equipped with a bilinear form B is the set W⊥ of all vectors in V that are...

In computability theory, a set of natural numbers is called computable, recursive, or decidable if there is an algorithm which takes a number as input...

Ramsey theory. A set is independent if and only if its complement is a vertex cover. Therefore, the sum of the size of the largest independent set α(G){\displaystyle...