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Single Idea 15925

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers ]

Full Idea

Each Von Neumann ordinal number is the set of its predecessors. ...He had shown how to introduce ordinal numbers as sets, making it possible to use them without leaving the domain of sets.

Gist of Idea

Each Von Neumann ordinal number is the set of its predecessors

Source

report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Shaughan Lavine - Understanding the Infinite V.3

Book Ref

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.122

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The 5 ideas from 'On the Introduction of Transfinite Numbers'

12336

A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]

13489

Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]

18180

Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]

18179

For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]

15925

Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]