Set theory is a basic branch of mathematics, and its research object is general set. Set theory occupies a unique position in mathematics, and its basic concepts have penetrated into all fields of mathematics. 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".

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.

Introduction:

Set theory is a branch of mathematics that studies the structure, operation and properties of sets. Modern mathematics, the most important basic theory, was founded by Cantor in 1970s and 1980s. A set of points on a plane (or space) is called a "point set". A point set can be some isolated points, or all points on a curve or region.

We can regard all kinds of geometric figures as a point set, and then study the identity characteristics of the points contained in it from the relationship between position and quantity, so that we can often get deeper conclusions than intuition. The basic theory of point set is called point set theory, while set theory discusses a more extensive and abstract general set than point set.

Set theory is widely used in various branches of mathematics, such as geometry, algebra, analysis, probability theory, mathematical logic and programming languages. The elements of a set should satisfy some axioms.

Various axiomatic systems of set theory can be established, such as the first axiomatic system of set theory (ZF system) proposed by Zermelo (E. zermelo, Germany,1871-KLOC-0/953), so as to avoid the Russell paradox from 65438 to 65438. The important problems about the basis of set theory have not been satisfactorily solved so far.