more from George Cantor

Single Idea 18174

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

Full Idea

Cantor's second innovation was to extend the sequence of ordinal numbers into the transfinite, forming a handy scale for measuring infinite cardinalities.

Gist of Idea

Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities


report of George Cantor (works [1880]) by Penelope Maddy - Naturalism in Mathematics I.1

Book Reference

Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.17

A Reaction

Struggling with this. The ordinals seem to locate the cardinals, but in what sense do they 'measure' them?