more from John von Neumann

### Single Idea 12336

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers]

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]**