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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.
1. Naive set theory can mean set theory developed non-rigorously without axioms 2. Naive set theory can mean the inconsistent theory with the axioms of extensionality and comprehension 3. Naive set theory is an introductory book on set theory by Halmos natural The natural sum and natural product of ordinals are the Hessenberg sum and product NCF
Pocket set theory; Positive set theory; S (Boolos 1989) Scott–Potter set theory; Tarski–Grothendieck set theory; Von Neumann–Bernays–Gödel set theory; Zermelo–Fraenkel set theory; Zermelo set theory; Set (mathematics) Set-builder notation; Set-theoretic topology; Simple theorems in the algebra of sets; Subset; Θ (set theory) Tree ...
In many formal set theories, such as Zermelo–Fraenkel set theory, set builder notation is not part of the formal syntax of the theory. Instead, there is a set existence axiom scheme, which states that if E is a set and Φ(x) is a formula in the language of set theory, then there is a set Y whose members are exactly the elements of E that ...
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.
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Set 3-1 has three possible rotations/inversions; the normal form (left) is the most compact, corresponding to the smallest sector. In musical set theory, a Forte number is the pair of numbers Allen Forte assigned to the prime form of each pitch class set of three or more members in The Structure of Atonal Music (1973, ISBN 0-300-02120-8). The ...