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.

The empty set is the set containing no elements.

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.


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