Real numbers include rational numbers and irrational numbers. Among them, irrational numbers are infinitely cyclic decimals, and rational numbers include integers and fractions.

Mathematically, real numbers are intuitively defined as numbers corresponding to points on the number axis. Originally, real numbers were just numbers, but later the concept of imaginary numbers was introduced. The original numbers were called "real numbers"-meaning "real numbers".

Real numbers can be divided into rational numbers and irrational numbers, or algebraic numbers and transcendental numbers, or positive numbers, negative numbers and zero. A set of real numbers is usually represented by the letter r or r n, and r n represents an n-dimensional real number space. Real numbers are uncountable. Real number is the core research object of real analysis.

Real numbers can be used to measure continuous quantities. Theoretically, any real number can be expressed as an infinite decimal, and to the right of the decimal point is an infinite series (cyclic or acyclic). In practice, real numbers are often approximate to a finite decimal (n digits are reserved after the decimal point, and n is a positive integer). In the computer field, because computers can only store a limited number of decimal places, real numbers are often represented by floating-point numbers.

(1) inverse number (only two numbers with different signs, we will say that one of them is the inverse number of the other) The inverse number of the real number A is-a.

② Absolute value (the distance between a point corresponding to a number on the number axis and the origin 0) The absolute value of the real number A is: │ A │ = ① When a is a positive number, | A | = A

② When a is 0, |a|=0.

③ When a is negative, | a | =-a.

③ Reciprocal (the product of two real numbers is 1, so these two numbers are reciprocal) The reciprocal of real number A is: 1/a (a≠0).

Edit the historical source of this paragraph.

Egyptians began to use fractions as early as around 1000 BC. Around 500 BC, Greek mathematicians headed by Pythagoras realized the necessity of irrational numbers. Indians invented negative numbers around 600 AD. It is said that China also invented negative numbers, but it was a little later than Indian.

It was not until17th century that real numbers were widely accepted in Europe. 18th century, calculus was developed on the basis of real numbers. It was not until 187 1 that German mathematician Cantor put forward the strict definition of real numbers for the first time.