1. Real number is the general term for rational numbers and irrational numbers.
Real numbers are defined as numbers corresponding to real numbers and points on the number line. Real numbers can be intuitively viewed as finite decimals and infinite decimals, and real numbers correspond to points on the number axis. But the whole of real numbers cannot be described by enumeration alone. Real numbers and imaginary numbers are both complex numbers. Real numbers can be divided into two categories: rational numbers and irrational numbers, or algebraic numbers and transcendental numbers. The set of real numbers is usually represented by the bold letter R. R represents n-dimensional real number space. Real numbers are uncountable. Real numbers are the core research object of real number theory.
The set of all real numbers can be called the real number system (real number system) or the 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 represented by R. Since R is an operating system that defines arithmetic operations, it is called the real number system.
2. Imaginary numbers
Imaginary numbers refer to complex numbers other than real numbers, among which imaginary numbers with a real part of 0 are called pure imaginary numbers.
In mathematics, an imaginary number is a number of the form a+b*i, where a and b are real numbers, and b≠0,i? = - 1. The term imaginary numbers was coined by Descartes, a famous mathematician in the 17th century, because the concept at that time was that they were real numbers that did not exist. Later, it was discovered that the real part a of the imaginary number a+b*i can correspond to the horizontal axis on the plane, and the imaginary part b corresponds to the vertical axis on the plane. In this way, the imaginary number a+b*i can correspond to the point (a, b) in the plane. .
The imaginary number bi can be added to the real number a to form a complex number of the form a + bi, where the real numbers a and b are called the real and imaginary parts of the complex number, respectively. Some authors use the term pure imaginary to refer to so-called imaginary numbers, which represent any complex number with a nonzero imaginary part.
Extended information:
In 1777, the Swiss mathematician Euler (Euler, or translated as Euler) began to use the symbol i to represent the unit of imaginary numbers. Later generations organically combined imaginary numbers and real numbers and wrote them in the form a+bi (a and b are real numbers, when a is equal to 0, it is called a pure imaginary number, when ab is not equal to 0, it is called a complex number, and when b is equal to 0, it is a real number). Usually, we use the symbol C to represent the set of complex numbers and the symbol R to represent the set of real numbers.
Baidu Encyclopedia - Imaginary Numbers
Baidu Encyclopedia - Real Numbers