# Empty set

In mathematics, the **empty set** is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.[1] Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set.

Any set other than the empty set is called *non-empty*.

In some textbooks and popularizations, the empty set is referred to as the "null set".[1] However, *null set* is a distinct notion within the context of measure theory, in which it describes a set of measure zero (which is not necessarily empty). The empty set may also be called the *void set*.