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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 ...
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.
In mathematics, the algebra of sets, not to be confused with the mathematical structure of an algebra of sets, defines the properties and laws of sets, 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 ...
In set theory and its applications throughout mathematics, a class is a collection of sets ... Monk, Donald J. (1969), Introduction to Set Theory, ...
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.
Lectures in set theory, with particular emphasis on the method of forcing, Springer-Verlag Lecture Notes in Mathematics 217 (1971) (ISBN 978-3540055648) The axiom of choice, North-Holland 1973 (Dover paperback edition ISBN 978-0-486-46624-8) (with K. Hrbáček) Introduction to set theory, Marcel Dekker, 3rd edition 1999 (ISBN 978-0824779153)
Philosophy portal; Mathematics portal; Set theory is any of a number of subtly different things in mathematics:. Naive set theory is the original set theory developed by mathematicians at the end of the 19th century, treating sets simply as collections of things.
For more about elementary set theory, see set, set theory, algebra of sets, and naive set theory. For an introduction to set theory at a higher level, see also axiomatic set theory, cardinal number, ordinal number, Cantor–Bernstein–Schroeder theorem, Cantor's diagonal argument, Cantor's first uncountability proof, Cantor's theorem, well ...