An empty set is a subset of any set, and an empty set is a proper subset of any non-empty set, but an empty set is not a subset of an empty set, because any two equal sets can only be subsets of each other, not proper subset.

For two non-empty sets, we can judge subsets and proper subset by their element subordination. The empty set has no elements, so there are special regulations in this respect, and there is no need to delve into the reasons.

Extended data:

When two circles are separated, the set of their common points is an empty set; When the discriminant value of the root of a quadratic equation in one variable △

Empty sets can only be transformed into topological spaces in one way, that is, by defining empty sets as open sets; This empty topological space is the only initial object of topological space category with continuous mapping.

An empty set is the proper subset of any non-empty set. ? There is only one subset, and there is no proper subset. {? } has two subsets, one is? One is itself.