more from Shaughan Lavine

Single Idea 15915

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity]

Full Idea

The ordinals are basic because the transfinite sets are those that can be counted, or (equivalently for Cantor), those that can be numbered by an ordinal or are well-ordered.

Gist of Idea

Ordinals are basic to Cantor's transfinite, to count the sets


Shaughan Lavine (Understanding the Infinite [1994], III.4)

Book Reference

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.54

A Reaction

Lavine observes (p.55) that for Cantor 'countable' meant 'countable by God'!

Related Idea

Idea 15916 Frege's one-to-one correspondence replaces well-ordering, because infinities can't be counted [Frege, by Lavine]