In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects...

a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory...

In mathematics, more specifically in point-set topology, the derived set of a subset S {\displaystyle S} of a topological space is the set of all limit...

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,...

any of some sets "Complement and Set Difference". web.mnstate.edu. Retrieved 2020-09-04. "Complement (set) Definition (Illustrated Mathematics Dictionary)"...

empty set. For explanation of the symbols used in this article, refer to the table of mathematical symbols. The union of two sets A and B is the set of elements...

logic Set theory – Branch of mathematics that studies sets Number theory – Branch of mathematics Combinatorics – Branch of discrete mathematics Finite...

In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be...

In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic...

In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains...

In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. For example, given a set called A containing...

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...

(the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation...

In mathematics, when the elements of some set S {\displaystyle S} have a notion of equivalence (formalized as an equivalence relation), then one may naturally...

The History of Mathematics: An Introduction include how to define "elements" or parts of a set, how to define unique elements in the set, and how to prove...

formulas. Commonly encountered mathematical objects include numbers, expressions, shapes, functions, and sets. Mathematical objects can be very complex;...

In mathematics, a singleton (also known as a unit set or one-point set) is a set with exactly one element. For example, the set { 0 } {\displaystyle \{0\}}...

examines the implementation of mathematical concepts in set theory. The implementation of a number of basic mathematical concepts is carried out in parallel...

because it is not itself a set. Universe (mathematics) Grothendieck universe Domain of discourse Von Neumann–Bernays–Gödel set theory — an extension of...

bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers...

In mathematics, an uncountable set, informally, is an infinite set that contains too many elements to be countable. The uncountability of a set is closely...

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...

combinatorial mathematics. Boston: Addison-Wesley. p. 143. ISBN 978-0-201-72634-3. Johnson, David L. (2001). "3.3 Laws". Elements of logic via numbers and sets. Springer...

symbols used in this article, refer to the table of mathematical symbols. The intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted...

the standard form of axiomatic set theory and as such is the most common foundation of mathematics. Zermelo–Fraenkel set theory with the axiom of choice...

In 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...

set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set...

In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently...

equivalent over ZF set theory. The goal of reverse mathematics, however, is to study possible axioms of ordinary theorems of mathematics rather than possible...

{Z} ,n=2k\}} The set of all even integers, expressed in set-builder notation. In mathematics and more specifically in set theory, set-builder notation...