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Herbert Bruce Enderton (April 15, 1936 – October 20, 2010) [1] was an American mathematician. He was a Professor Emeritus of Mathematics at UCLA and a former member of the faculties of Mathematics and of Logic and the Methodology of Science at the University of California, Berkeley .
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.
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 ...
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 set theory, a branch of mathematics, an urelement or ur-element (from the German prefix ur-, 'primordial') is an object that is not a set (has no elements), but that may be an element of a set. It is also referred to as an atom or individual. Ur-elements are also not identical with the empty set.
Set is the prototype of a concrete category; other categories are concrete if they are "built on" Set in some well-defined way. Every two-element set serves as a subobject classifier in Set. The power object of a set A is given by its power set, and the exponential object of the sets A and B is given by the set of all functions from A to B.
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.
Von Neumann–Bernays–Gödel set theory (NBG) is a commonly used conservative extension of Zermelo–Fraenkel set theory that does allow explicit treatment of proper classes. There are many equivalent formulations of the axioms of Zermelo–Fraenkel set theory. Most of the axioms state the existence of particular sets defined from other sets.
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