more from George Cantor

### Single Idea 18173

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity]

Full Idea

Cantor's first innovation was to treat cardinality as strictly a matter of one-to-one correspondence, so that the question of whether two infinite sets are or aren't of the same size suddenly makes sense.

Gist of Idea

Cardinality strictly concerns one-one correspondence, to test infinite sameness of size

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

It makes sense, except that all sets which are infinite but countable can be put into one-to-one correspondence with one another. What's that all about, then?