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Set theory is the branch of mathematical logic that studies sets, ... In the US in the 1960s, the New Math experiment aimed to teach basic set theory, ...
Basic concepts in infinite set theory (1 C, 13 P) F. Families of sets (2 C, 67 P) G. Graphical concepts in set theory (5 P) O. Operations on sets (1 C, 11 P) P.
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
It is the algebra of the set-theoretic operations of union, intersection and complementation, and the relations of equality and inclusion. For a basic introduction to sets see the article on sets, for a fuller account see naive set theory, and for a full rigorous axiomatic treatment see axiomatic set theory.
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
Von Neumann–Bernays–Gödel set theory (NBG) is a commonly used conservative extension of Zermelo–Fraenkel set theory that does allow explicit treatment of proper classes. There are many equivalent formulations of the axioms of Zermelo–Fraenkel set theory. Most of the axioms state the existence of particular sets defined from other sets.
Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. [3] Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language.
basic set theory 1. Naive set theory 2. A weak set theory, given by Kripke–Platek set theory without the axiom of collection. Sometimes also called "rudimentary set theory". [1] BC Berkeley cardinal BD Borel determinacy Berkeley cardinal
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