The empty set, or void set, is the unique set having no elements, so its cardinality is zero. Some axiomatic set theories guarantee that the empty set exists by including an explicit axiom of the empty set, while in others its existence can be deduced from other axioms, and many possible properties of sets hold vacuously true for it. Any set other than the empty set is called non-empty. The empty set is sometimes called the null set in textbooks and popular accounts, but null set is a distinct notion in measure theory, where it denotes a set of measure zero that is not necessarily empty.
Facts
Origin YearDates the introduction of the modern empty-set symbol by the Bourbaki group (Andre Weil) in 1939; the underlying concept of a set with no elements is far older and is not given a specific year in the source. Connections
Associated With
Attributed To
Source Empty Set (Wikipedia)
In Branch
Sources
1. Empty Set (Wikipedia)
Wikimedia FoundationLead section
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.
Notation
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 WITH STROKE) in the Danish and Norwegian alphabets.
Attributed To: André Weil, Lead
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 WITH STROKE) in the Danish and Norwegian alphabets
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