1872, the German mathematician Dai Dejin started from the requirement of continuity, defined irrational numbers through the division of rational numbers, and established the theory of real numbers on a strict scientific basis, thus ending the era when irrational numbers were regarded as "irrational numbers" and the first great crisis in the history of mathematics that lasted for more than two thousand years.
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The origin of irrational numbers:
Pythagoras was a great mathematician in ancient Greece. He proved many important theorems, including Pythagorean theorem named after him, that is, the sum of the square areas of both sides of a right triangle is equal to the square area of the hypotenuse.
In 500 BC, hippasus, a disciple of the Pythagorean school, discovered an amazing fact, that is, the diagonal length of a square is not commensurate with its side length (if the side length of a square is 1, the diagonal length is not a rational number), which is the "everything" of the Pythagorean school. The philosophy of numbers is completely different.
The discovery of the Hebrews revealed the defects of the rational number system for the first time and proved that it cannot be equated with a continuous infinite straight line. Rational numbers are not filled with points on the number axis, and there are "holes" on the number axis that cannot be expressed by rational numbers. This kind of "pore" was proved to be "countless" by later generations.
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