Non-empty 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 "${\displaystyle \{\}}$", "∅", and "${\displaystyle \emptyset }$". 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, "${\displaystyle 0}$" was occasionally used as a symbol for the empty set.

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