"∅" redirects here. For similar symbols, see Ø (disambiguation).
For other uses of "Empty", see Empty (disambiguation).
In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.[1] Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set.
Any set other than the empty set is called non-empty.
In some textbooks and popularizations, the empty set is referred to as the "null set".[1] However, null set is a distinct notion within the context of measure theory, in which it describes a set of measure zero (which is not necessarily empty).
^ abWeisstein, Eric W. "Empty Set". mathworld.wolfram.com. Retrieved 2020-08-11.
mathematics, the emptyset is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure...
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of real numbers and the emptyset—the unique set containing no elements. The emptyset is also occasionally called the null set, though this name is ambiguous...
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codomain R {\displaystyle \mathbb {R} } (the set of all real numbers), this implies that the diameter of the emptyset (the case S = ∅ {\displaystyle S=\varnothing...
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is a set with no members at all. Because a set is determined completely by its elements, there can be only one emptyset. (See axiom of emptyset.) Although...
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set is defined inductively as the smallest ordinal number greater than the ranks of all members of the set. In particular, the rank of the emptyset is...