Set is an undefined concept. While understanding the concept of set, we should grasp the properties of certainty, mutual difference and disorder of elements in set, and we can use these properties to solve problems. Pay attention to the relationship between elements and sets, and whether the relationship between sets is inclusive or not can not be confused. To skillfully perform the operations of intersection, union and complement of sets, when the set contains letters, the set should be simplified first.

Collection is the basis of high school mathematics, and it is also one of the contents of the college entrance examination. The idea of set and set language can penetrate into all branches of high school mathematics, and can be examined together with many knowledge such as functions, equations and inequalities. When solving a problem, we need to know the set language first, convert the set language into mathematical language, and then solve the problem with relevant knowledge.

2. Understand the three properties of elements in a set.

(1) certainty

The elements in the collection must be deterministic. For sets and elements, one or both must be in one place. For example, "all numbers greater than 100" form a set, and the elements in the set are certain. But a "larger integer" cannot form a set because its object is uncertain. For example, "larger tree" and "larger integer" cannot form a set.

(2) Anisotropy

For a given collection, the elements in the collection must be different. When any two identical objects are in the same set, they can only be counted as an element in this set. For example, if the collection consists of, the value of cannot be or 1.

(3) Disorder

The order of the elements in the collection is out of order. For example, a set consists of sets or can be written as a set, and they all represent the same set.

3. Problems that should be paid attention to when learning set representation.

(1) Pay attention to the difference between and. It is an element in the collection, but the collection contains an element. The relationship between them is.

(2) Pay attention to the difference between and. It is a set without any elements, but a set with elements.

(3) When enumerating sets, you must not make the mistake of using {real number set} or expressing real number set, because the "braces" here already contain the meaning of "all".

When describing a set with characteristic properties, we should pay special attention to what the elements in this set are and what characteristic properties it should have, so as to accurately understand the meaning of the set. For example:

The elements in a set are the solution set of a binary equation represented by this set, or understood as a point set composed of points on a curve;

The elements in the set are, this set represents the value range of the independent variables in the function;

The elements in the set are, this set represents the range of function values in the function;

There is only one element in a set (equation), which is a single-element set represented by enumeration.

4. Comments on the relationship between set and set operation.

(1) Note the difference between and: ""indicates the relationship between elements and sets, such as. ""indicates the relationship between sets, such as.

(2) Understand the meaning of "harmony": "including" and ",and one and only one is true; And ""is equivalent to "and".

(3) Try to use venn diagram to express the relationship between two sets, gradually form a way of thinking about and thinking about problems from the perspective of sets, learn the problem-solving skills of classifying and writing all subsets of a given set, and find out the relationship between the number of elements in a set and the number of all subsets by exploring the exercises in the textbook Exploration and Research.

(4) The definition and operation of intersection, union, complete set and complement set are the key points of this part, which can be understood by combining with venn diagram, and attention should be paid to venn diagram's intuitive role.

(5) Pay attention to the characteristics of using empty sets. An empty set is a special set, which is a subset of any set. Using this characteristic of empty set, we can correctly solve some problems that imply empty set conditions.

(6) The function of complementary set in set operation can not be ignored. If it is difficult to solve a problem from the front, we can start from the opposite side of the problem, that is, adopt the idea of complement set.