In mathematics, the empty set is the unique set having no elements, or a cardinality of zero. It is unique because in set theory, two sets are equal if they have the same elements. As a result there can only be one set with no elements – *the* (not *an*) empty set.

The empty set is usually denoted {} or .

**Properties**

- The empty set is a subset of all sets.
- The union of a set with the empty set is the set itself.
- The intersection of any set with the empty set is the empty set.
- The Cartesian product of any set and the empty set is the empty set.