### Single Idea 15897

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

Full Idea

Zermelo realised that the Axiom of Choice (based on arbitrary functions) could be used to 'count', in the Cantorian sense, those collections that had given Cantor so much trouble, which restored a certain unity to set theory.

Gist of Idea

Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed

Source

report of Ernst Zermelo (Proof that every set can be well-ordered [1904]) by Shaughan Lavine - Understanding the Infinite I

Book Reference

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.4

Related Idea

Idea 15896
Cantor needed Power Set for the reals, but then couldn't count the new collections **[Cantor, by Lavine]**