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The unique set having no elements.
The empty set is used as the von Neumann realization of zero, but that identification is a chosen encoding rather than an intrinsic meaning of zero.
wp-empty-setnlab-empty-setopenlogic-set-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Select the unique set having no elements.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-empty-setopenlogic-set-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
ZF proves that a set with no elements exists and extensionality proves that it is unique.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-zfwp-empty-setopenlogic-set-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The von Neumann convention uses the empty set as the set-theoretic representative of the abstract numeral .
Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.
wp-von-neumann-ordinalnlab-natural-number