The Meaning and Representation of 1. 1 Set
Emphasis and difficulty: the meaning and expression method of set, expressing mathematical objects or mathematical contents in set language; Distinguish between elements and sets and their symbolic representations; Use set language (description method) to express mathematical objects or mathematical contents; Correct selection of set representation.
Requirements: ① Understand the meaning of set and the "subordinate" relationship between elements and set;
Natural language, graphic language and set language (enumeration or description) can be used to describe different specific problems.
Classic example: If x∈R, what conditions should the element x in {3, x, x2-2x} meet?
Classroom exercises:
1. Among the four objects given below, () constitutes a set.
A. the taller student in class a. B. the approximate value of the long-lived person C. the reciprocal is equal to his own number
2. The following four propositions are correct ()
The set of prime numbers in a. a. 10 is {0, 3, 5, 7} b. 1, and the set consisting of 2, 3 can be expressed as {1, 2, 3} or {3, 2, 1}.
C. The solution set of the equation is {1, 1}. D.0 and {0} represent the same set.
3. The following four propositions: (1) The smallest number in set n is1; (2) if -a Z，a Z；
(3) All positive real numbers form a set r+; (4) Set A can be composed of very small numbers;
There are () correct propositions.
A. 1
4. The following four propositions: (1) Zero belongs to an empty set; (2) The solution set of equation x2-3x+5=0 is an empty set;
(3) The solution set of equation x2-6x+9=0 is a unit set; ④ inequality 2x-6 >；; The solution set of 0 is infinite;
There are () correct propositions.
A. 1
5. The set of all points in the second quadrant in the plane rectangular coordinate system is ()
A.{x, y and} B. {(x, y)}
C.{(x，y)} D. {x，y and}
6. Fill in the blanks with symbols or:
0 _ _ _ _ _ _ _ _ _ { 0 }，_ _ _ _ _ _ _ _ _ _ { a }，_ _ _ _ _ _ _ _ _ _ _ _ _ Q，_______Z，- 1 _ _ _ _ _ _ _ _ _ R，0 _ _ _ _ _ _ _ _ _ N，0。
7. The set composed of all even numbers can be expressed as {}.
8. The set D={} is represented by enumeration.
9. When a is satisfied, the set A = {} represents the unit set.
10. for the set A = {2 2,4,6}, if a A is 6-A A, the value of a is _ _ _ _ _ _ _.
What values can't X take in 1 1. number set {0, 1, x2-x}?
12. Set A = {x n | n} is known, and set A is represented by enumeration.
13. The known set A={}.
(1) If there is only one element in A, find the value of A; (2) If there is at most one element in A, find the value range of A. 。
14. Let a set A consisting of real numbers meet the conditions: if A is a and A is 1, it is proved that:
(1) If 2 A, there must be two other elements in set A. Find out these two elements;
(2) There are at least three different elements in non-empty set A ... References:
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