Real number is a general term for rational number and irrational number. Mathematically, a real number is defined as the number corresponding to a point 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.

The basic operations that real numbers can realize are addition, subtraction, multiplication, division, multiplication and so on. For non-negative numbers (that is, positive numbers and 0), you can also perform a root operation. The result of addition, subtraction, multiplication, division (divisor is not zero) and square of real numbers is still real numbers. Any real number can be raised to an odd power, and the result is still a real number. Only non-negative real numbers can be raised to even powers, and the result is still real numbers.

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The source of real numbers

Around 500 BC, Greek mathematicians headed by Pythagoras realized that rational numbers could not meet the needs of geometry, but Pythagoras himself did not admit the existence of irrational numbers. It was not until17th century that real numbers were widely accepted in Europe. 18th century, calculus was developed on the basis of real numbers. 187 1 year, German mathematician Cantor first put forward a strict definition of real numbers.

From ancient Greece to17th century, mathematicians gradually accepted the existence of irrational numbers and regarded them as equal numbers with rational numbers. Later, the concept of imaginary number was introduced to show the difference, which means "real number". At that time, although imaginary number appeared and was widely used, the strict definition of real number was still a problem. Until the concepts of function, limit and convergence were clarified, Dai Dejin, Cantor and other talents at the end of19th century strictly dealt with real numbers.

Baidu Encyclopedia-Real Numbers