Full Idea
In Von Neumann's definition an ordinal is a transitive set in which all of the elements are transitive.
Clarification
See Idea 12337 for 'transitive set'
Gist of Idea
A von Neumann ordinal is a transitive set with transitive elements
Source
report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Alain Badiou - Briefings on Existence 11
Book Reference
Badiou,Alain: 'Briefings on Existence', ed/tr. Madarsz,Norman [SUNY 2006], p.128
Related Idea
Idea 12337 There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou]