Real number is a general term for rational number and irrational number. Mathematically, real numbers are defined as the number of corresponding points on the number axis. Real numbers can be intuitively regarded as one-to-one correspondence between finite decimals and infinite decimals, and between real numbers and points on the number axis. But the whole of real numbers can't be described only by enumeration. Real and imaginary numbers * * * make up a complex number.

Real numbers can be divided into rational and irrational numbers, or algebraic and transcendental numbers. Real number sets generally use black letters? r？ Express delivery. R stands for n-dimensional real number space. Real numbers are uncountable. Real number is the core research object of real number theory.

The set of all real numbers can be called real number system or real number continuum. Any complete Archimedean ordered field can be called a real number system. It is unique in the sense of order-preserving isomorphism, and is often expressed by R. Because R is an arithmetic system that defines arithmetic operations, it is called the real number system.

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Mathematical analysis, also known as advanced calculus, is the oldest and most basic branch of analysis. Generally speaking, it refers to a relatively complete mathematical subject with the general theory of calculus and infinite series as the main content, including their theoretical basis (basic theory of real number, function and limit). It is also a basic course for college mathematics majors.

The branch of analysis in mathematics is a branch of mathematics that specializes in studying real numbers and complex numbers and their functions. Its development began with calculus and extended to the continuity, differentiability and integrability of functions. These characteristics help us to study the material world and discover the laws of nature.