Set theory or set theory is a mathematical theory to study a set (a whole composed of a bunch of abstract objects), including the most basic mathematical concepts such as set, element and subordinate relationship. In most formulas of modern mathematics, set theory provides the language of how to describe mathematical objects. Set theory and isomorphism between logic and first-order logic form the axiomatic basis of mathematics, and mathematical objects are formally constructed with undefined terms such as "set" and "set members". Set theory occupies a unique position in mathematics, and its basic concepts have penetrated into all fields of mathematics.

In naive set theory, set is considered as a self-proving concept, such as a whole composed of a bunch of objects.

In axiomatic set theory, set and set members are not directly defined, but some axioms that can describe their properties are standardized first. Under this idea, sets and set members, like points and lines in Euclidean geometry, have no direct definition.

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A collection refers to a collection of concrete or abstract objects with certain attributes, which are called elements of a collection. For example, the collection of all China people, its element is every China person. We usually use uppercase letters such as A, B, S, T, ... to represent the set, and lowercase letters such as A, B, X, Y, ... to represent the elements in the set. ? If X is an element of the set S, it is said that X belongs to S and is marked as X ∈ S ... If Y is not an element of the set S, it is said that Y does not belong to S and is marked as y &；; #87 13; S generally, we call a set with finite elements a finite set, and a set with infinite elements an infinite set.