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Nonempty set


In mathematics, and more specifically set theory, 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.

Null set was once a common synonym for "empty set", but is now a technical term in measure theory. The empty set may also be called the void set.

Common notations for the empty set include "", "∅", and "". The latter two symbols were introduced by the Bourbaki group (specifically André Weil) in 1939, inspired by the letter Ø in the Norwegian and Danish alphabets (and not related in any way to the Greek letter Φ). Although now considered an improper use of notation, in the past, "" was occasionally used as a symbol for the empty set.


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