The meaning of 1. set

2. Three characteristics of elements in a set:

(1) element determinism,

(2) Anisotropy of elements,

(3) the disorder of elements,

3. Representation of assembly: {…} For example, {basketball players in our school}, {Pacific Ocean, Atlantic Ocean, Indian Ocean, Arctic Ocean}

(1) The set is expressed in Latin letters: A={ basketball players in our school}, B={ 1, 2, 3, 4, 5}.

(2) Representation of sets: enumeration and description.

Note: Commonly used digit sets and their symbols:

The set of nonnegative integers (i.e. natural number set) is denoted as n.

Positive integer set N* or N+ integer set z rational number set q real number set r

1) enumeration: {A, b, C...}

2) Description: A method of describing the common attributes of elements in a collection and writing them in braces to represent the collection. {x？ r | x-3 & gt； 2}，{ x | x-3 & gt； 2}

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

4) Venn diagram:

4, the classification of the set:

The (1) finite set contains a set of finite elements.

(2) An infinite set contains an infinite set of elements.

(3) An example of an empty set without any elements: {x | x2 =-5}

Second, the basic relationship between sets

1. "Inclusive" relation-subset

Note: There are two possibilities that A is a part of B (1); (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. Answer? A

② proper subset: If a? B and a? B then says that set A is the proper subset of set B, and writes it as A B (or B A).

3 if a? B，B？ C, then a? C

4 if a? At the same time? 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.

Third, the operation of the set.

Complement set of intersection and union of operation types

Defined by all elements belonging to A and B, it is called the intersection of A and B, and marked as A B (pronounced' A crosses B'), that is, AB = {X | X A, and X B}.

A set consisting of all elements belonging to set A or set B is called the union of A and B. Note: A B (pronounced as' A and B'), that is, A B ={x|x A, or X B}).

Let S be a set, A is a subset of S, and the set of all elements in S that do not belong to A is called the complement (or complement) of subset A in S.

Remember, that's

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