Rank (set theory)

In mathematical set theory, the rank of a set is defined inductively as the smallest ordinal number greater than the rank of any member of the set, where the rank of the empty set is zero. As a consequence, when using the normal set-theoretic definition of the ordinal numbers in terms of sets, every ordinal has a rank equal to itself.

Related Topics:
Set theory - Inductively - Ordinal number - Empty set

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