Ideas from 'Proof that every set can be well-ordered' by Ernst Zermelo [1904], by Theme Structure

[found in 'From Frege to Gödel 1879-1931' (ed/tr Heijenoort,Jean van) [Harvard 1967,0-674-32449-8]].

green numbers give full details    |     back to texts     |     unexpand this idea


6. Mathematics / A. Nature of Mathematics / 5. The Infinite / e. Countable infinity
Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed
                        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.
                        From: report of Ernst Zermelo (Proof that every set can be well-ordered [1904]) by Shaughan Lavine - Understanding the Infinite I