First, the basic relationship between sets.

1. subset of "inclusive" relation.

Note: There are two possibilities.

(1)A is a part of B.

(2)A and B are the same set.

On the other hand, set A is not included in set B, or set B does not include set A, so it is recorded as A B or B A.

2. "Equality" relationship: A=B (5≥5 and 5≤5, then 5=5).

Example: let a = {x | x2-1= 0} b = {-1,1} "Two sets are equal if their elements are the same".

Namely: ① Any set is a subset of itself. AA .

② proper subset: If A B, and A B, then set A is the proper subset of set B, denoted as AB (or B A).

③ If AB, BC, then AC.

(4) If AB is also BA, then A = B. ..

3. A set without any elements is called an empty set and recorded as φ.

It is stipulated that an empty set is a subset of any set and an empty set is a proper subset of any non-empty set.

A set of n elements, including 2n subsets and 2n- 1 proper subset.

Second, set and its representation.

1, the meaning of set.

The word "assembly" first reminds us of the "all-round assembly" that teachers often call when going to physical education class or having a meeting. The meaning of "set" in mathematics is the same as this, except that one is a verb and the other is a noun.

So the meaning of a set is: some specified objects are gathered together to form a set, which is called a set for short, and each object is called an element. For example, the collection of Grade One and Grade Two, then all the students in Grade One and Grade Two form a collection, and each student is called the element of this collection.

2. Representation of sets.

Generally, sets are represented by uppercase letters, and elements are represented by lowercase letters, such as set A={a, b, c}. A, B and C are elements in set A, marked as A ∈ A; conversely, D does not belong to set A and is marked as dA.

There are some special sets to remember:

Non-negative integer set (i.e. natural number set) n positive integer set n or N+.

Integer set z rational number set q real number set r.

Representation of collections: enumeration and description.

① enumeration method: {a, b, c...}.

(2) Description: Describe the common attributes of the elements in the collection. Such as {xr | x-32}, {x | x-32}, {(x, y) | y = x2+ 1}.

③ Language description: Example: {A triangle that is not a right triangle}.

Example: the solution set of inequality x-32 is {xr | x-32} or {x | x-32}.

Key point: the descriptive representation of a set should pay attention to the representative elements of the set.

A={(x, y)|y= x2+3x+2} is different from B={y|y= x2+3x+2}. There are array elements (x, y) in set A, while there is only element Y in set B. ..

3. Three characteristics of 3.set.

(1) disorder.

Refers to the arrangement of elements in a set without order, such as set A={ 1, 2} and set B={2, 1}, then set A = B.

Example: let A={ 1, 2} and B={a, b}. If A=B, find the values of a and b.

Solution: a = B.

Note: There are two solutions to this problem.

(2) Mutual anisotropy.

It means that the elements in the collection cannot be repeated, and a = {2,2} can only be expressed as {2}.

③ certainty.

The certainty of a set means that the nature of the elements that make up the set must be clear, and ambiguity and ambiguity are not allowed. (1), high school mathematics function knowledge summary (2), high school mathematics function knowledge summary (3), high school mathematics compulsory examination knowledge summary (4), high school mathematics knowledge summary and formula summary encyclopedia (5), high school mathematics compulsory examination knowledge summary formula encyclopedia (6), college entrance examination mathematics knowledge summary and problem-solving ideas (7), NMET compulsory examination knowledge summary and summary (8)