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
Source
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?