Single Idea 14445

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX]

Full Idea

The [Axiom of Choice] is also equivalent to the assumption that of any two cardinals which are not equal, one must be the greater.

Gist of Idea

Choice shows that if any two cardinals are not equal, one must be the greater

Source

Bertrand Russell (Introduction to Mathematical Philosophy [1919], XII)

Book Reference

Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.124


A Reaction

It is illuminating for the uninitiated to learn that this result can't be taken for granted (with infinite cardinals).