A number in the form of z = A+bi(A and B are both real numbers) is called a complex number, where A is called the real part, B is called the imaginary part, and I is called the imaginary part. When the imaginary part of z is equal to zero, z is often called a real number; When the imaginary part of z is not equal to zero and the real part is equal to zero, z is often called pure imaginary number.

2. Real numbers

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. But the whole of real numbers can't be described only by enumeration. Real and imaginary numbers * * * make up a complex number.

3. Rational number

Rational number is the collective name of integer (positive integer, 0, negative integer) and fraction, and it is the set of integer and fraction.

Extended data:

Understanding of rational numbers;

Rational number is a general term for integer (positive integer, 0, negative integer) and fraction. Positive integers and fractions are collectively referred to as positive rational numbers, and negative integers and fractions are collectively referred to as negative rational numbers. Therefore, the number of rational number sets can be divided into positive rational numbers, negative rational numbers and zero.

Since any integer or fraction can be converted into a cyclic decimal, and vice versa, every cyclic decimal can also be converted into an integer or fraction, so a rational number can also be defined as a cyclic decimal.

The set of rational numbers is an extension of the set of integers. In the set of rational numbers, the four operations of addition, subtraction, multiplication and division (divisor is not zero) are unimpeded.

Provisions on the order of magnitude of rational numbers A and B: If a-b is a positive rational number, it is said that when A is greater than B or B is less than A, it is marked as A >；; B or b < a. Any two unequal rational numbers can compare sizes.

An important difference between rational number set and integer set is that rational number set is dense while integer set is dense. After arranging rational numbers in order of size, there must be other rational numbers between any two rational numbers, which is density. Integer sets do not have this feature, so there are no other integers between two adjacent integers.

Rational numbers are compact subsets of real numbers: every real number has a rational number that is arbitrarily close. A related property is that only rational numbers can be transformed into finite continued fractions. Rational numbers have an ordered topology according to their sequences. Rational number is a (dense) subset of real number, so it also has subspace topology. ?

Baidu encyclopedia-rational number

Baidu encyclopedia-plural

Baidu Encyclopedia-Real Numbers