Empty set

In mathematics, and more specifically set theory, the empty set is the unique set having no (zero) members. Some axiomatic set theories assure 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 trivially true for the empty set. Null set was once a common synonym for "empty set," but this usage should should be avoided because "null set" is now a technical term in measure theory. Common notations for the empty set include "{}," "" and "" The latter two symbols were introduced by the Bourbaki group (specifically Andre Weil) in 1939, inspired by the letter Ø in the Danish and Norwegian alphabet. Other notations for the empty set include "Λ", "0", and "‣" By the principle of extensionality, two sets are equal if they have the same elements; therefore there can be only one set with no elements. Hence there is but one empty set, and we speak of "the empty set" rather than "an empty set." ... full article at wikipedia