Is an empty set a finite set? What is an empty set?

Definition: A collection without any elements becomes an empty set. Representation: Represented by symbols.

Considering that the empty set is a subset of a real line (or arbitrary topological space), the empty set is both an open and a closed set. The set of boundary points of an empty set is an empty set, which is a subset of it, so an empty set is a closed set.

The set of inner points of an empty set is also an empty set and is a subset of it, so an empty set is an open set. Also, because all finite sets are compact, empty sets are compact sets. A closure of an empty set is an empty set.

Empty set example: 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 is <0, the set of its real roots is also an empty set.

In axiomatic set theories such as Zemero-Frankl set theory, the existence of empty sets is determined by the axioms of empty sets. The uniqueness of the empty set is derived from the axiom of extension. With the axiom of separation, any axiom that states the existence of a set will imply the axiom of the empty set.

For example, if a is a set, then the axiom of separation allows the construction of a set, which can be defined as an empty set.

The empty plane itself is a collection. It's just that this set doesn't have any elements, and I can count how many there are (there are zero). So, of course, it's a limited set.

An empty set has 0 elements, 0 is finite, and all belong to a finite set.

Doesn't a finite set have an exact number of elements? And an empty set has no elements, how can it be a finite set?

The details are as follows:

1. When two circles are separated, the set of their common points is an empty set;

2. When the discriminant value of the root of a quadratic equation is <0, the set of its real roots is also an empty set.

An empty set is a collection that does not contain any elements. An empty set is a subset of any set and is a true subset of any non-empty set. An empty set is not none; It is a collection with no elements inside.

Think of a set as a bag with elements, and the bag of an empty set is empty, but the bag itself does exist.

Partial nature of empty sets:

1. The only subset of the empty set is the empty set itself: a, if a a, then a= a, if a= then a a.

2. For any set a, the empty set is a subset of a: a: a.

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

4. For any non-empty set a, the empty set is a true subset of a: a,,, if a≠ then true is contained in a.

5. For any set a, the intersection of the empty set and a is an empty set: a, a

Because an empty set is covered with a curly brace to indicate a set that contains an element, which is . But it's not an empty set, because it contains an element. Without parentheses, it is a notice that represents an empty set, i.e. a set without any elements.

An empty set is a collection that does not contain any elements. An empty set is a subset of any set and is a true subset of any non-empty set. An empty set is not none; It is a collection with no elements inside.