Empty set (Wikipedia)

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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.

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The Mount Baker Highway was constructed by Whatcom County in 1893 as a wagon road traveling northeast from Bellingham along the Nooksack River through Deming and Kendall to Maple Falls.

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2023-10-31

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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”.

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https://en.wikipedia.org/wiki/Empty_set

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