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Ideas for 'fragments/reports', 'Meaning and Reference' and 'A Tour through Mathematical Logic'

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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers

13530	An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS]
	Full Idea: Less theoretically, an ordinal is an equivalence class of well-orderings. Formally, we say a set is 'transitive' if every member of it is a subset of it, and an ordinal is a transitive set, all of whose members are transitive.
	From: Robert S. Wolf (A Tour through Mathematical Logic [2005], 2.4)
	A reaction: He glosses 'transitive' as 'every member of a member of it is a member of it'. So it's membership all the way down. This is the von Neumann rather than the Zermelo approach (which is based on singletons).