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... 34 KB (4,715 words) - 07:25, 14 February 2024 |
Naive set theory for the mathematical topic. Naive Set Theory is a mathematics textbook by Paul Halmos providing an undergraduate introduction to set... 6 KB (903 words) - 17:44, 13 November 2023 |
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... 9 KB (1,262 words) - 02:59, 23 February 2024 |
generators. The paradoxes of naive set theory can be explained in terms of the inconsistent tacit assumption that "all classes are sets". With a rigorous foundation... 8 KB (1,180 words) - 15:49, 26 February 2024 |
Russell's paradox (redirect from Set of all sets that do not contain themselves) Russell's paradox. The term "naive set theory" is used in various ways. In one usage, naive set theory is a formal theory, that is formulated in a first-order... 31 KB (4,602 words) - 15:51, 18 April 2024 |
Element (mathematics) (redirect from Element (set theory)) MR 0319684. "Sets - Elements | Brilliant Math & Science Wiki". brilliant.org. Retrieved 2020-08-10. Halmos, Paul R. (1974) [1960], Naive Set Theory, Undergraduate... 7 KB (798 words) - 08:58, 22 February 2024 |
discovery of paradoxes in naive set theory, such as Russell's paradox, led to the desire for a more rigorous form of set theory that was free of these paradoxes... 47 KB (6,252 words) - 07:04, 26 April 2024 |
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. The... 15 KB (1,865 words) - 20:37, 23 February 2024 |
contradiction in naive set theory. This paradox is avoided in axiomatic set theory. Although it is possible to represent a proposition about a set as a set, by a... 17 KB (2,672 words) - 17:37, 18 April 2024 |
Curry's paradox (category Paradoxes of naive set theory) self-referential sentences, certain forms of naive set theory are still vulnerable to Curry's paradox. In set theories that allow unrestricted comprehension... 15 KB (2,427 words) - 22:54, 18 March 2024 |
Boolean algebra (section Naive set theory) Boolean algebra with 2n elements. Naive set theory interprets Boolean operations as acting on subsets of a given set X. As we saw earlier this behavior... 73 KB (9,405 words) - 16:23, 27 April 2024 |
Infinite". mathworld.wolfram.com. Retrieved 2020-09-05. Halmos, Paul, Naive Set Theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted by Springer-Verlag... 6 KB (826 words) - 03:33, 12 January 2024 |
paradox in naïve set theory. naive set theory 1. Naive set theory can mean set theory developed non-rigorously without axioms 2. Naive set theory can mean... 91 KB (11,499 words) - 13:50, 27 April 2024 |
In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, it can be proven in multiple... 10 KB (1,322 words) - 07:21, 7 February 2024 |
of set theory is no more than these properties. For more about elementary set theory, see set, set theory, algebra of sets, and naive set theory. For... 5 KB (545 words) - 19:21, 25 July 2023 |
theory Naive set theory S (set theory) Kripke–Platek set theory Scott–Potter set theory Constructive set theory Zermelo set theory General set theory... 1 KB (127 words) - 18:06, 8 February 2024 |
Naive Bayes classifier, a simple probabilistic classifier Naive set theory, a non-axiomatic approach to set theory, in mathematics Search for "naive"... 2 KB (264 words) - 21:55, 23 December 2023 |
specified set of attributes Relation (mathematics) – Relationship between two sets, defined by a set of ordered pairs Halmos, P. R. (1960), Naive Set Theory, Undergraduate... 2 KB (319 words) - 15:36, 16 May 2023 |
Axiom schema of specification (category Axioms of set theory) Foundations and positive set theory use different restrictions of the axiom of comprehension of naive set theory. The Alternative Set Theory of Vopenka makes... 11 KB (1,669 words) - 09:13, 10 January 2024 |
Inductive Constructions. Type theory was created to avoid a paradox in a mathematical equation based on naive set theory and formal logic. Russell's paradox... 59 KB (7,861 words) - 20:13, 22 March 2024 |
Fiber (mathematics) (redirect from Fiber (naive set theory)) y} under a function f{\displaystyle f} is the preimage of the singleton set {y}{\displaystyle \{y\}},: p.69 that is f−1({y})={x:f(x)=y}{\displaystyle... 6 KB (832 words) - 08:53, 10 April 2024 |
Symmetric difference (redirect from Symmetric difference (set theory)) (1963) Applications of Graph Theory to Group Structure, page 16, Prentice-Hall MR0157785 Halmos, Paul R. (1960). Naive set theory. The University Series in... 16 KB (2,399 words) - 21:23, 5 March 2024 |
Burali-Forti paradox (category Paradoxes of naive set theory) have an order type Ω {\displaystyle \Omega } . It is easily shown in naïve set theory (and remains true in ZFC but not in New Foundations) that the order... 6 KB (880 words) - 20:27, 11 March 2024 |