Concept of subset: For two non-empty sets A and B, if any element of set A is an element of set B, we say A? B (pronounced as a contained in b), or b? A (pronounced as b containing a) means that set A is a subset of set B.

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

A subset of an empty set is itself.

If a? B, and at least one element in set B does not belong to set A, then set A is called the proper subset of set B, and any set is a subset of itself.

Extended data

for instance

1, the collection of all Asian countries is the collection of all countries on earth in proper subset; The set of all natural numbers is the proper subset of the set of all integers (that is, n? z)； { 1, 3} ? { 1, 2, 3, 4},{ 1, 2, 3} ? { 1, 2, 3, 4}; {? }。 But you can't say {1, 2,3}? { 1, 2, 3}。 ?

2. Let the complete set I be {1, 2,3}, then its subsets can be {1}, {2}, {3}, {1, 2}, {1, 3} and {2,3}. And its proper subset can only be {1}, {2}, {3}, {1, 2}, {1, 3}, {2,3},? . Its non-empty proper subset can only be {1}, {2}, {3}, {1, 2}, {1, 3}, {2,3}.

A set without any elements is called an empty set, an empty set is a subset of any set, and an empty set is a proper subset of any non-empty set.

Any set is a subset of itself, and non-proper subset is the original set.

An empty set is a subset of any set, and a non-empty proper subset is a subset except the empty set and the original set.

References:

Baidu Encyclopedia-a subset of Baidu Encyclopedia-proper subset