1) The set of all nonnegative integers is usually called the nonnegative integer set (or natural number set). 0, 1, 2, 3, 4 ...0 and positive integers are natural numbers.

1994 1 1 In the People's Republic of China (PRC) National Standard, Mathematical Symbols Used in Physical Science and Technology issued by the State Bureau of Technical Supervision, natural number set was recorded as:

N={0， 1，2，3，…}

2) Positive integers and negative integers are collectively referred to as integers. All real numbers, including 0 (that is, numbers without imaginary parts) are integers. ...-3 -2 - 1 0 1 2 3 ...

Integer set: z = {...-3,-2,-1,0,1,2, 3 ...}

3) Rational number: a number that can be accurately expressed as the ratio of two integers. Integers and fractions are collectively called rational numbers. This fraction can also be expressed as a finite decimal or an infinite cyclic decimal.

For example, 3, -98. 1 1, 5.7272 ... and 7/22 are rational numbers. Rational numbers can also be divided into positive rational numbers, negative rational numbers and 0.

All rational numbers form a set, that is, rational number set, which is represented by bold letter Q, while some modern math books are represented by hollow letter Q.

4) pi = 3. 14 1592653 ...

Another example is: 0. 1 01001001… (there is one more zero between two1).

None of the above figures are finite decimals or infinite cyclic decimals, that is, they are infinite acyclic decimals. We call infinite cyclic decimals irrational numbers.

Note: (1) Irrational number must meet three conditions: ① is decimal; ② is an infinite decimal; ③ No cycle.

(2) Irrational numbers are not all numbers with radical signs (for example, π is irrational numbers), and conversely, numbers with radical signs are not necessarily irrational numbers.

5) Rational numbers and irrational numbers are collectively called real numbers.

Real number set: the set of all real numbers.

The set of rational numbers includes integers and fractions, that is, except infinite cyclic decimals.

Real numbers, including rational numbers and irrational numbers, are positive numbers, negative numbers and zero.

There are about six groups of commonly used numbers: integer set, natural number set rational number set, irrational number set, real number set and imaginary number set.

Imaginary set, needless to say. . .