empty set

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Foggy view from Pigeon Point (1 of 2)

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∅ is the empty set shining through reality
Eventually, you will find the empty set.
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 result, there can be only one set with no elements, hence the usage of “the empty set” rather than “an empty set”.

tags

axiomatic set theory
mathematics

Wikidata

https://www.wikidata.org/wiki/Q226183

Wikipedia

Empty set (Wikipedia) In mathematics, 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, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set.