### Single Idea 13492

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers]

Full Idea

It is easier to generalize von Neumann's finite ordinals into the transfinite. All Zermelo's nonzero finite ordinals are singletons, but if ω were a singleton it is hard to see how if could fail to be the successor of its member and so not a limit.

Gist of Idea

Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton

Source

William D. Hart (The Evolution of Logic [2010], 3)

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.75