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How are mathematical numbers classified? What are real numbers, rational numbers, irrational numbers, integers and natural numbers? What numbers are included?
The types of numbers come from the needs of people's practice. Natural numbers represent people's initial understanding of logarithms and are the reflection of complete individuals. Integers include negative integers, 0 and positive integers, among which negative integers are an abstraction in mathematics, and their introduction enables people to describe the objective world with simple mathematical symbols. Later, it was found that sometimes an individual can still divide. At this time, it is more convenient to introduce the concept of rational number, which can be written as a fraction, that is, it can be expressed as a finite decimal or an infinite circulating decimal. Later, it was found that some numbers may not necessarily represent the form of component quantities, but these numbers can be obtained through the operation of rational numbers (such as Pythagorean theorem). These numbers are irrational numbers, and irrational numbers are infinite acyclic decimals, which cannot express the form of fractions. Rational numbers and irrational numbers are collectively called real numbers, which can be represented by a straight line with direction and scale, that is, the number axis. There is a one-to-one correspondence between real numbers and points on the number axis. The introduction of imaginary numbers is similar to the introduction of negative numbers relative to positive numbers, and it is also a mathematical abstraction. This abstraction expands the concept of number from one-dimensional real axis to two-dimensional complex plane, and through abstraction, the objective world can be described by complex numbers. It can be considered that with the needs of people, all kinds of numbers will be abstracted, strictly defined and then applied to practice.