Full Idea
Cantor's set theory was not of collections in some familiar sense, but of collections that can be counted using the indexes - the finite and transfinite ordinal numbers. ..He treated infinite collections as if they were finite.
Gist of Idea
Cantor's theory concerns collections which can be counted, using the ordinals
Source
report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite I
Book Reference
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.3
Related Idea
Idea 15896 Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]