====================================================================== = Empty set = ====================================================================== Introduction ====================================================================== In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. In some textbooks and popularizations, the empty set is referred to as the "null set". However 'null set' is a distinct notion within the context of measure theory. In that setting, it describes a set of measure zero; such a set is not necessarily empty. The empty set may also be called the 'void set'. Common notations for the empty set