more on this theme | more from this text
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]
15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
13672 | All the axioms for mathematics presuppose set theory [Neumann] |
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] |
3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |