In mathematics, the empty set or void 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 See more

In standard axiomatic set theory, by the principle of extensionality, two sets are equal if they have the same elements (that is, neither of them has an element not in the other). As a … See more

Extended real numbers
Since the empty set has no member when it is considered as a subset of any ordered set, every member of that set will be an upper bound and lower bound for the empty set. For example, when considered as a subset of the … See more

• 0 – Number
• Inhabited set – Property of sets used in constructive mathematics
• Nothing – Complete absence of anything; the opposite of everything
• Power set – Mathematical set containing all subsets of a given … See more

Common notations for the empty set include "{ }", "$${\displaystyle \emptyset }$$", and "∅". The latter two symbols were introduced by the Bourbaki group (specifically André Weil) in 1939, inspired by the letter Ø (U+00D8 Ø LATIN CAPITAL LETTER O … See more

Historical issues
In the context of sets of real numbers, Cantor used $${\displaystyle P\equiv O}$$ to denote "$${\displaystyle P}$$ contains no single point". This $${\displaystyle \equiv O}$$ notation was utilized in definitions; for … See more

• Halmos, Paul, Naive Set Theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted by Springer-Verlag, New York, 1974. See more