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Single Idea 13489

[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers ]

Full Idea

Von Neumann's decision was to start with the ordinals and to treat cardinals as a special sort of ordinal.

Gist of Idea

Von Neumann treated cardinals as a special sort of ordinal

Source

report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by William D. Hart - The Evolution of Logic 3

Book Ref

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.73

A Reaction

[see Hart 73-74 for an explication of this]

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]
18179 For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
18180 Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
15925 Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]