What is a real number (classification of real numbers) There are two types of real numbers.

First of all, we should know rational numbers, which can be expressed as integers, including integers and fractions. Decimals are infinite cycle decimals, because there are infinite zero cycles behind integers, so rational numbers are infinite cycle decimals.

At first, Pythagoras in ancient Greece put forward the concept that everything can be expressed by integers, but after Pythagoras theorem was put forward, hippasus found that the opposite sides of equilateral right triangle with 1 as the side could not be expressed by integers, and human beings realized the existence of irrational numbers for the first time, so the real number system was greatly expanded.

We later learned that irrational numbers not only exist, but also there are far more irrational numbers on the number axis than rational numbers. Moreover, many important mathematical constants are irrational numbers, such as pi, natural constant e, and irrational numbers can be expressed as infinite acyclic decimals.

To sum up, real numbers can be expressed in one sentence, that is, real numbers are infinite decimals, rational numbers are cyclic, and irrational numbers are acyclic.