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Ideas of John von Neumann, by Text
[Hungarian, 1903  1957, One of the fathers of the modern computer.]
1923

On the Introduction of Transfinite Numbers


p.24

18180

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


p.24

18179

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


p.73

13489

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


p.122

15925

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


p.128

12336

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

1925

An Axiomatization of Set Theory


p.209

13672

All the axioms for mathematics presuppose set theory


p.215

15943

Limitation of Size is not selfevident, and seems too strong [Lavine]


p.188

3355

Von Neumann wanted mathematical functions to replace sets [Benardete,JA]


p.280

3340

Von Neumann defines each number as the set of all smaller numbers [Blackburn]
