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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 .
Naive Set Theory is a mathematics textbook by Paul Halmos providing an undergraduate introduction to set theory. [1] Originally published by Van Nostrand in 1960, [ 2 ] it was reprinted in the Springer-Verlag Undergraduate Texts in Mathematics series in 1974.
As set theory gained popularity as a foundation for modern mathematics, there has been support for the idea of introducing the basics of naive set theory early in mathematics education. In the US in the 1960s, the New Math experiment aimed to teach basic set theory, among other abstract concepts, to primary school students, but was met with ...
Further, since set theory was seen as the basis for an axiomatic development of all other branches of mathematics, Russell's paradox threatened the foundations of mathematics as a whole. This motivated a great deal of research around the turn of the 20th century to develop a consistent (contradiction-free) 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 ...
Alternative set theory; Axiomatic set theory; Kripke–Platek set theory with urelements; Morse–Kelley set theory; Naive set theory; New Foundations; Positive set theory; Zermelo–Fraenkel set theory; Zermelo set theory; Set (mathematics) Simple theorems in the algebra of sets; Subset; Θ (set theory) Tree (descriptive set theory) Tree (set ...
In mathematical logic, an alternative set theory is any of the alternative mathematical approaches to the concept of set and any alternative to the de facto standard set theory described in axiomatic set theory by the axioms of Zermelo–Fraenkel set theory.
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.