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) - 04:23, 9 June 2024
Naive set theory for the mathematical topic. Naive Set Theory is a mathematics textbook by Paul Halmos providing an undergraduate introduction to set...
13 KB (2,182 words) - 13:00, 17 August 2024
considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of naive set theory. After the discovery...
41 KB (5,021 words) - 06:29, 26 July 2024
combinations of sets Naive set theory – Informal set theories Symmetric difference – Elements in exactly one of two sets Union (set theory) – Set of elements...
12 KB (1,482 words) - 10:00, 8 May 2024
formulation of naïve set theory, the properties of sets have been defined by axioms. Axiomatic set theory takes the concept of a set as a primitive notion...
41 KB (4,747 words) - 09:15, 3 July 2024
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...
9 KB (1,275 words) - 14:29, 6 June 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...
46 KB (6,267 words) - 22:43, 15 August 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 (4,600 words) - 20:26, 24 July 2024
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
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) - 19:43, 12 July 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
technique Naive set theory – Informal set theories Symmetric difference – Elements in exactly one of two sets Union – Set of elements in any of some sets "Intersection...
12 KB (1,737 words) - 23:16, 26 December 2023
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) - 16:28, 28 May 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 (796 words) - 08:53, 30 June 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...
16 KB (2,428 words) - 14:13, 27 June 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 (1,327 words) - 06:43, 21 May 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) - 10:05, 6 August 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...
75 KB (9,506 words) - 17:24, 21 June 2024
mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed...
20 KB (2,425 words) - 23:34, 3 April 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 (11,511 words) - 21:47, 23 May 2024
and Modern, Oxford University Press, pp. 7–37 Halmos, Paul (1960). Naive Set Theory R. Springer. p. 28. ISBN 9780387900926. Lucas, John F. (1990). Introduction...
14 KB (1,881 words) - 00:43, 18 June 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 (7,869 words) - 13:25, 12 August 2024
In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The...
40 KB (5,391 words) - 19:53, 22 June 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) - 06:32, 23 May 2024
simple axioms, GST is also immune to the three great antinomies of naïve set theory: Russell's, Burali-Forti's, and Cantor's. GST is Interpretable in relation...
9 KB (1,187 words) - 11:57, 21 July 2024
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...
15 KB (2,169 words) - 20:46, 14 August 2024
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
Cantor's paradox (category Paradoxes of naive set theory)
nature of infinity and the notion of a set. Put another way, it is paradoxical within the confines of naïve set theory and therefore demonstrates that a careless...
5 KB (734 words) - 07:41, 20 November 2023
56–57. ISBN 3-540-13258-9. Retrieved 8 January 2023. Paul Halmos, Naive set theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted by Springer-Verlag...
4 KB (633 words) - 21:31, 22 March 2024