What are natural number sets, rational number sets, real number sets, and how many number sets are there

What are natural number sets, rational number sets, real number sets, and how many number sets are there

These four sets are commonly used: natural number set, integer set, rational number set and real number set
1) The set of all non negative integers is usually referred to as the set of non negative integers (or set of natural numbers) ". 0, 1, 2, 3, 4 0 and positive integers are natural numbers
In the national standard of the people's Republic of China, mathematical symbols used in physical science and Technology issued by the State Bureau of Technical Supervision in November 1994, the set of natural numbers is recorded as:
　　　　N={0,1,2,3,… }
2) Positive integers and negative integers are called integers. All real numbers including 0 are integers
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 circular decimal
For example, 3, - 98.11, 5.7272 Rational numbers can also be divided into positive rational numbers, negative rational numbers and 0
All rational numbers form a set, that is, the set of rational numbers, which is represented by the bold letter Q. some more modern mathematics books are represented by the hollow letter Q
4) Pi = 3.141592653 ,
Another example: 0.1010010001 There is a zero between the two 1s
These numbers are not finite decimals or infinite cyclic decimals, that is, they are not rational numbers. They are all infinite non cyclic decimals. We call infinite non cyclic decimals irrational numbers
Note: (1) irrational number should meet three conditions: ① is a decimal; ② is an infinite decimal; ③ does not cycle
(2) Irrational numbers are not always numbers with roots (for example, π is irrational numbers), on the contrary, numbers with roots are not necessarily irrational numbers
5) Rational numbers and irrational numbers are called real numbers
Set of real numbers: the set of all real numbers
The set of rational numbers includes integers and fractions, that is, except for infinite acyclic decimals
Real numbers, including rational and irrational numbers, are positive, negative and zero
There are about six number sets commonly used. Integer set, natural number set, rational number set, irrational number set, real number set, imaginary number set
Imaginary number set, needless to say