Representation: using symbols? (note:? (pronounced oe) is a Latin letter, which is different from the Greek letter φ (pronounced fi) or {}. (Note: { } is a set with empty elements, not an empty set)

For any set a, an empty set is a subset of a;

Some things don't exist, they are empty sets.

A: A.

For any set a, the union of empty set and a is a:

A: A ∨? = A

For any set a, the intersection of an empty set and a is an empty set:? A: A ∩? = ?

For any set a, an empty set and the cartesian product of a are empty sets;

A: A×? = ?

The only subset of an empty set is the empty set itself:

A: A? A =？

The number of elements in an empty set (that is, its potential) is zero; In particular, the empty set is limited:

| ? | = 0

For a complete set, the complement of an empty set is a complete set:

Cu？ =U

In set theory, two sets are equal if they have the same elements; Then only one set can have no elements, that is, the empty set is unique.

Considering that an empty set is a subset of a real number line (or any topological space), it is both an open set and a closed set. The boundary point set of an empty set is an empty set and its subset, so an empty set is a closed set. The interior point set of an empty set is also an empty set and a subset of it, so an empty set is an open set. In addition, an empty set is a compact set because all finite sets are compact.

The closure of an empty set is an empty set.

Press Alt on the computer, and then press 02 16 to print the empty set symbol?

Definition of empty set: A set without any elements is called an empty set.

The essence of empty set: an empty set is a subset of all sets. An empty set is the proper subset of any non-empty set.