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

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, including integers). 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 (there are only two numbers with different signs, and their sum is zero, so we say that one of them is the inverse number of the other). The inverse number of the real number A is -a, and the distances between A and -a on the number axis are equal to the origin 0. )

2) Absolute value (another number is equal to the distance from A to the origin 0 on the number axis) The absolute value of the real number A is |a|

① When a is a positive number, |a|=a (constant)

② When a is 0, |a|=0.

③ When a is negative, | a | =-a(a (the inverse of a)

The absolute value of any number is greater than or equal to 0, because the distance is not negative. )

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).

4) number axis (any real number can be represented on the number axis. )

Definition: if you draw a straight line, define the right direction as the positive direction of the straight line, and take the origin o and unit length OE on it, it will become a number axis, or a number axis.

Three elements of (1) axis: origin, positive direction and unit length.

(2) There is a one-to-one correspondence between points on the number axis and real numbers. [ 1]

5) square root (the result of square multiplication is a real number equal to [√], in which the square root belonging to a non-negative real number is called the arithmetic square root. Positive numbers have two square roots; 0 has only one square root, which is 0 itself; Negative numbers have no square root. )

6) Cubic root (if the cube of a number X is equal to A, that is, the cubic of X is equal to A (X 3 = A), that is, X is equal to A three times in a row, then this number X is called the cube root of A, also called the cube root).