generally, a collection of any sets whatsoever is called a family of sets, set family, or a set system. Additionally, a family of sets may be defined as a...

sets. A set may be finite or infinite. There is a unique set with no elements, called the empty set; a set with a single element is a singleton. Sets...

sources this is a set of sets, while other sources allow it to be a multiset of sets, with some sets repeated. An indexed family of sets ( A i ) i ∈ I ,...

Branch of mathematics concerning probability Ring of sets – Family closed under unions and relative complements Set function – Function from sets to numbers...

sets have been released per year, in addition to various spin-off products. Magic has made three types of sets since Alpha and Beta: base/core sets,...

if and only if every family of closed subsets with F.I.P. is fixed. Filter (set theory) – Family of sets representing "large" sets Mac Lane, Saunders;...

(X)} will denote the power set of X . {\displaystyle X.} A subset of a power set is called a family of sets (or simply, a family) where it is over X {\displaystyle...

two different notions of a ring of sets, both referring to certain families of sets. In order theory, a nonempty family of sets R {\displaystyle {\mathcal...

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 an element of A and b...

However, families differ from sets in that the same object can appear multiple times with different indices in a family, whereas a set is a collection of distinct...

consequences; in particular, by defining different collections of sets containing 0 (distinct from the sets (−ε, ε)), one may find different results regarding the...

countable family of closed sets of uniqueness is a set of uniqueness. There exists an example of two sets of uniqueness whose union is not a set of uniqueness...

sets in some finite family of sets have a union that also belongs to the family, must some element belong to at least half of the sets in the family?...

algebra of sets, not to be confused with the mathematical structure of an algebra of sets, defines the properties and laws of sets, the set-theoretic...

The sets in P are said to exhaust or cover X. See also collectively exhaustive events and cover (topology). The intersection of any two distinct sets in...

combinatorics, a Helly family of order k is a family of sets in which every minimal subfamily with an empty intersection has k or fewer sets in it. Equivalently...

measurable sets. They are closed under operations that one would expect for measurable sets, that is, the complement of a measurable set is a measurable set and...

mathematics, the Erdős–Ko–Rado theorem limits the number of sets in a family of sets for which every two sets have at least one element in common. Paul Erdős,...

The Family Star is a 2024 Indian Telugu-language romantic action drama film written and directed by Parasuram, and produced by Dil Raju and Sirish under...

collection is typically called an indexed family, often written as {Aj}j∈J. An enumeration of a set S gives an index set J ⊂ N {\displaystyle J\subset \mathbb...

List of South Indian film families. For Indian music families, see List of Indian music families. The Akhtar family is a prominent film family in the...

parameters Family of sets, a collection of sets Indexed family, a family where each element can be given an index Normal family, a collection of continuous...

compactness in terms of closed sets; this is its most prominent application. Other applications include proving that certain perfect sets are uncountable,...

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

mathematics, the cylinder sets form a basis of the product topology on a product of sets; they are also a generating family of the cylinder σ-algebra. Given...

Mitford family is an aristocratic British family who became particularly well known in the 1930s for the six Mitford sisters, the daughters of David Freeman-Mitford...

extends to any collection of sets. A collection of sets is pairwise almost disjoint or mutually almost disjoint if any two distinct sets in the collection are...

Mathematical construction of a set with an equivalence relation Transversal (combinatorics) – Set that intersects every one of a family of sets Devlin 2004, p. 122...

Wisconsin. The Working Families Party was first organized in 1998 by a coalition of labor unions, community organizations, members of the now-inactive national...

{P} (S)} , or 2S. Any subset of P(S) is called a family of sets over S. If S is the set {x, y, z}, then all the subsets of S are {} (also denoted ∅ {\displaystyle...