more on this theme | more from this text
Full Idea
Von Neumann's version of the natural numbers is in fact preferred because it carries over directly to the transfinite ordinals.
Gist of Idea
Von Neumann numbers are preferred, because they continue into the transfinite
Source
comment on John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n9
Book Ref
Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.24
| 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] |
| 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] |
| 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] |
| 22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
| 3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
| 3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |