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Set
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Set A selection of articles related to Set

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set, Set, Set - Cardinality of a set, Set - Complements, Set - Definition, Set - Describing sets, Set - Intersections, Set - Special sets, Set - Subsets, Set - Unions, Set - Descriptions using mathematical notation, Set - Descriptions using words or lists, Set - Set membership, Alternative set theory, Class (set theory), Family (mathematics), Mathematical structure, Multiset, Tuple

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ARTICLES RELATED TO Set

Set: Encyclopedia - Set

In mathematics, a set can be thought of as any collection of distinct things considered as a whole. Though a simple idea, it is nevertheless one of the most important and fundamental concepts in modern mathematics, and the study of the structure of possible sets, set theory, is quite rich. Set theory, having only been invented at the end of the 19th century, is now a ubiquitous part of mathematics education, being introduced as early as primary school. It is the language in which modern mathematics is described. Set theory can be viewed as the foundation upon which nearly all of mathematics can be built and the source from wh ...

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Set: Encyclopedia II - Set - Describing sets Set - Descriptions using words or lists. Not all sets have precise descriptions of any sort; they may simply be arbitrary collections, with no expressible "rule" saying what elements are in or out. Some sets may be described in words, for example: A is the set whose members are the first four positive whole numbers. B is the set whose members ar ...

In topology and related branches of mathematics, a closed set is a set whose complement is open. This implies that a closed set contains its own boundary; the most familiar example of a closed set is the closed interval [a,b] of real numbers. Intuitively, if you are outside the set, and you "wiggle" a little bit, you will still be outside the set. Note that this notion depends on the concept of "outside", the surrounding space with respect to which the complement is taken. For instance, the unit interval [0,1] is closed ...

Set: Encyclopedia - Breathing set

Breathing set. For breathing apparatus used underwater, see scuba sets and rebreather and surface supplied diving. For breathing apparatus used out of water, see SCBA. For breathing apparatus used in space, also see spacesuit. Sometimes the term "breathing apparatus" is used for an animal's respiratory system. Other related archivesSCBA, rebreather, respiratory system, scuba sets, spacesuit, surface supplied diving

Set: Encyclopedia - Analytic set

Given a Polish space X, a subset is analytic if there is a Polish space Y and a Borel set such that A is the projection of B; that is, Note that the choice of the Polish space Y above is not very important; it could be replaced in the definition by a fixed uncountable Polish space, say Baire space or Cantor space or the real lin ...

Set: Encyclopedia - Class set theory

In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. Some classes are sets (for instance, the class of all integers that are even), but others are not (for instance, the class of all ordinal numbers or the class of all sets). A class that is not a set is called a proper class. A proper class cannot be an element of a set or a class and is not subject to the Zermelo-Fr ...

Set: Encyclopedia - Box set

A box set (or boxed set) refers to one or more recordings, movies and television programs that are contained in a "box" made generally out of cardboard. Box set - Notable music recording box sets. (list in order of release date) Bruce Springsteen & the E Street Band Live/1975-85 - Bruce Springsteen (1986) Crossroads - Eric Clapton (1988) The Beatles Box Set - The Beatles (1988) The Good, the Bad and the Live - Metallica ( ...

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Read more here: » Box set: Encyclopedia - Box set

Set: Encyclopedia - Autocatalytic set

An autocatalytic set is a collection of entities, each of which is able to catalyze the creation of others within the set, such that as a whole, the set is able to catalyze its own replication. In this way the set as a whole is said to be autocatalytic. Autocatalytic sets were originally and most concretely defined in terms of entities which are replicating molecules, but have more recently been metaphorically exte ...

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Set: Encyclopedia - Convex set

In Euclidean space, an object is convex if for any pair of points within the object, any point on the straight line segment that joins them is also within the object. For example, a solid cube is convex, but anything that is hollow or has a dent in it is not convex. Convex set - Convex sets. Let C be a set in a real or complex vector space. C is said to be convex if, for all x and y in C and all t in the interval [0,1], the point (1 − t) ...

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Convex set - Convex sets

Convex set - Properties of convex sets

Convex set - Orthogonal convexity

Convex set - Abstract axiomatic convexity

Set: Encyclopedia - Countable set

In mathematics the term countable is used to describe the size of a set, i.e. the number of elements it contains. The notion of an infinite set is not elementary; it requires a strong sense of abstraction and precision. A set is called countable if the number of elements is finite or if it has the same number of elements as the natural numbers. (Cantor defined a countable set as a set which can be put into one-to-one correspondence with a subset of the natural numbers). The term countable stems from the fac ...

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Set: Encyclopedia - Age set

In anthropology, an age set is a social category or corporate social group, consisting of people of similar age, who have a common identity, maintain close ties over a prolonged period, and together pass through a series of age-related statuses. This is in contrast to an age grade, through which people pass individually over time. While a year group or class in a school could be regarded as a simple example of an age set (e.g. 'Class of 2004'), the term is most commonly used to refer to systems in tribal societies. The phenomen ...

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Age set - A typical example

Read more here: » Age set: Encyclopedia - Age set

Set: Encyclopedia - Algebra of sets

The algebra of sets develops and describes the basic properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality (mathematics) and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations. Algebra of sets - Introduction. The algebra of sets is the development of the fundamental properties of set operations and set relations. These properti ...

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Set: Encyclopedia - Alternative set theory

Generically, an alternative set theory is an alternative mathematical approach to the concept of set. It is a proposed alternative to the standard set theory. Some of the alternative set theories are: the theory of semisets; rough set theory; fuzzy set theory. the set theory New Foundations Positive set theory Specifically, Alternative Set Theory (or AST) refers to a particular set theory developed in the 1970s and 1980s by Petr Vopěnka and his ...

Set: Encyclopedia - Union set theory

In set theory and other branches of mathematics, the union of a collection of sets is the set that contains everything that belongs to any of the sets, but nothing else. This article uses mathematical symbols. Union set theory - Basic definition. If A and B are sets, then the union of A and B is the set that contains all elements of A and all elements of B, but no other elements. The union of A and B is usually written "A ∪ B< ...

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Set: Encyclopedia - Complement set theory

In set theory and other branches of mathematics, two kinds of complements are defined, the relative complement and the absolute complement. Complement set theory - Relative complement. If A and B are sets, then the relative complement of A in B, also known as the set-theoretic difference of B and A, is the set of elements in B, but not in A. The relative complement of A in B is usually written Including:

Complement set theory - Relative complement

Complement set theory - Absolute complement

Set: Encyclopedia - Axiomatic set theory

Set theory is a branch of mathematics created principally by the German mathematician Georg Cantor at the end of the 19th century. Initially controversial, set theory has come to play the role of a foundational theory in modern mathematics, in the sense of a theory invoked to justify assumptions made in mathematics concerning the existence of mathematical objects (such as numbers or functions) and their properties. Formal versions of set theory also have a foundational role to play as specifying a theoretical ideal of mathematical rig ...

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Set: Encyclopedia - Separated sets

In topology and related branches of mathematics, separated sets are pairs of subsets of a given topological space that are related to each other in a certain way. The notion of when two sets are separated or not is important both to the notion of connected spaces (and their connected components) as well as to the separation axioms for topological spaces. Separated sets should not be confused with separated spaces (defined below), which are somewhat related but aren't the same thing. And separable spaces are a completely differe ...

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Set: Encyclopedia II - Set dance - The Set

Four couples are arranged in a square to dance, with each couple being in the middle of the sides of the square. Both the eight dancers in the group and the dance itself are called a 'set'. The dance is a sequence of several dance figures, which usually have a common theme or structure. The figures usually begin and end with repeated parts that everyone dances, and then during the figure each couple or pair of couples will dance separately. In the set, the couple with their backs to the band are traditionally named First Tops, with See also:

Set dance, Set dance - The Set, Set dance - External link

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