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...

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...

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

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...

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

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...

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...

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

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

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 = H...

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

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...

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...

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...

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...

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

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

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...

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

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

mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed...

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...

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

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

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

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...

of k {\displaystyle k} -subsets of an n {\displaystyle n} -element set. In set theory, the notation [ A ] k {\displaystyle [A]^{k}} is also common, especially...

intersection, and relative complement. Borel sets are named after Émile Borel. For a topological space X, the collection of all Borel sets on X forms a σ-algebra...