I. Collection of related concepts

1, meaning of set: some specified objects are set together into a set, and each object is called an element.

2. Three characteristics of elements in a set:

Element determinism; 2. Mutual anisotropy of elements; 3. The disorder of elements;

Description:

(1) For a given set, the elements in the set are certain, and any object is either an element of the given set or not.

(2) In any given set, any two elements are different objects. When the same object is contained in a collection, it is only an element.

(3) The elements in the set are equal and have no order. So to judge whether two sets are the same, we only need to compare whether their elements are the same, and we don't need to examine whether the arrangement order is the same.

(4) The three characteristics of set elements make the set itself deterministic and holistic.

3. Representation of set: {? Such as {basketball players in our school}, {Pacific Ocean, Atlantic Ocean, Indian Ocean, Arctic Ocean};

Use Latin letters to represent the set: a={ basketball players in our school}, b = {1, 2, 3, 4, 5};

Representation of collections: enumeration and description.

Note: Commonly used number 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.

Second, the basic relationship between sets

"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, which is marked as ab or ba.

"Equality" relation (5≥5 and 5≤5, then 5=5).

Example: let a = {x | x2-1= 0} b = {-1,1} "The elements are the same".

Conclusion: For two sets A and B, if any element of set A is an element of set B and any element of set B is an element of set A, we say that set A is equal to set B, that is, A = B.