What are natural number set, rational number set and real number set?

Natural numbers are 0,1,2,3,... Which are positive integers plus 0
A rational number is a finite decimal or an infinite circular decimal, which can be written as a rational fraction
Real numbers include rational numbers and irrational numbers

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1. What are natural number sets, rational number sets, real number sets, and how many number sets are there
2. The proof of the equality of cardinal number between algebraic number set and natural number set Don't prove that the set of rational numbers is countable there Let's not just say that algebraic numbers are countable because equations are countable
3. It is proved that the cardinality of rational number set in interval (0,1) is equal to that of natural number set!
4. Let a and B be set n of natural numbers, Mapping f: A to B maps element n in set a to element 2 ^ n + N in set B, then under mapping f, the original image of image 11 is
5. Let set a and set B be set n of natural numbers, and map f: a → B maps element n in set a to element 2n + N in set B, then under map f, the original image of image 20 is______ ．
6. Proof: (1 + A + A ^ 2 +...) +a^n）^2-a^n=(1+a+a^2+… +a^n-1)(1+a+a^2+… +A ^ n + 1), where is n natural number
7. Multiply by the power of the base, what if there is a number before the base For example: 2 (x + y) ^ 3 × (x + y) =? I know how to calculate the front one without 2, but I don't know if I add 2 Ask the prawns to help Please give the specific value
8. Under what conditions should we try to add exponentially with the same base
9. Exponents are the same, multiplication or addition? Add or multiply
10. -The reciprocal of the opposite number of 1 and 1 / 3 is? The absolute value is 2 and 1 / 3? The ratio size ↓ 1 (- 4) 3-3-4 power
11. There is a natural number with two digits. Three times the sum of the two digits is exactly the natural number. Find the natural number
12. 70 is divided into the sum of 11 different natural numbers. How many methods are there? List them one by one
13. How to construct the one to one correspondence between rational number and natural number set
14. The elements of set a are natural numbers If x ∈ a, then 4-x ∈ a 1. Write a set a with only one element 2. Write all sets a with 2 elements 3. How many sets a satisfy the condition of question setting
15. Is n a set of natural numbers or a set of positive integers?
16. Natural number set n positive integer set n + then does n + belong to n
17. When the elements in the set s are all natural numbers and satisfy the proposition "if x belongs to s, then 8-x belongs to s", how many sets S satisfy the above conditions When the elements in the set s are all natural numbers and satisfy the proposition "if x belongs to s, then 8-x belongs to s", how many sets S satisfy the above conditions, please write them all! I don't know the answer on the first floor
18. It is known that if x belongs to s, then 6-x belongs to s, the natural number x constitutes the set S1. If s is a set of single elements, then s=__ ,
19. When the elements in the set s are all natural numbers, and satisfy the proposition "if x belongs to s, then 8-x belongs to s", Try to write all of s with 3 elements? My question Why are there three elements? If you take 1, then 8-1 = 7, then 8-7 or return to 1, how can there be three elements?
20. If x belongs to s, then 8-x belongs to s If s has two elements, then s=