The reason for the formula of the number of subsets of a finite set

binomial theorem
It is equivalent to taking elements from n elements to form a new set
One is empty set, one of subsets
C(n,0)
Take an element, C (n, 1)
Take 2 elements, C (n, 2)
.
Take n elements, C (n, n)
The number of subsets is equal to C (n, 0) + C (n, 1) +. + C (n, n) = (1 + 1) ^ n = 2 ^ n

RELATED INFORMATIONS

1. What is the formula for subsets of numbers and non empty proper subsets,
2. Is an empty set a proper subset of all sets? Why? Some people say "non empty sets.",
3. An empty set is a proper subset of any set______ ．
4. What does it mean that an empty set is the only proper subset of a set? Make it clear. Take an example
5. If a subset of a contains n elements, how many subsets of a? How many nonempty subsets of a? How many nonempty proper subsets of a?
6. There are 2 ^ n subsets, 2 ^ n-1 nonempty subsets and 2 ^ n-2 nonempty proper subsets of set a with n elements What if n = 0
7. Set a has n elements, how many subsets of a and how many proper subsets of a
8. Parabola (definite integral) Find the parabola that passes through the point (0,0) and the axis of symmetry is parallel to the Y axis with the opening downward, so as to minimize the area enclosed by the X axis!
9. What are the quadrilaterals we've learned______ 、______ 、______ And______ ．
10. F1 (- 3,0) and F2 (3,0) are the two focal points of the ellipse x ^ 2 / A + y ^ 2 / b = 1. When p is on the ellipse, ∠ f1pf2 = 120 °, the triangle f1pf2 has the largest area, a + B I have worked out that s = √ 3B doesn't seem to have a maximum?
11. If there are n elements in set a, then set a has n elements______ Subset, yes______ A true subset, yes______ A nonempty proper subset
12. Write all subsets and proper subsets of set {a, B, C} Let's finish the problem by 22:00 this evening
13. If the set has 39 elements, then there are several non empty proper subsets. Remember that there is a formula, what is it?
14. How many subsets of set {1,2,3. N}, and how many subsets only contain five elements? Just answer the back empty
15. Find the set {1,2,3 n} The sum of the elements of all subsets of
16. Senior one mathematics compulsory 5, find the general formula In the sequence {an}, if A1 = 1 and an + 1 = 2An + 3, then the general term an of the sequence= Ask the master to give the answer, and give the steps!
17. Senior one mathematics compulsory five - find the general formula of the sequence! (1) 7,77,777,7777,. Find the general term formula of this sequence~ (2) The known sequence {an} is the arithmetic sequence, A1 = f (x + 1), A2 = 0, A3 = f (x-1), where f (x) = x ^ 2-4x + 2, find the general term formula It's mainly the first question! It doesn't matter if you can't work out the second one~
18. What I want is compulsory 3 knowledge points with examples
19. Fundamental theorem of plane vector If the point D is on the edge BC of the triangle ABC, and the vector CD = 4, the vector DB = m, the vector AB + N, the value of 3M + n Urgent..... Urgent..... Urgent..... Urgent..... Urgent..... Urgent..... Urgent..... Urgent..... Urgent..... Urgent..... Urgent..... Urgent..... Urgent..... Urgent..... Urgent
20. In △ ABC, B = 60 ° and B2 = AC, then the shape of △ ABC is_______ ．