Single Idea 14446

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

Full Idea

Among boots we distinguish left and right, so we can choose all the right or left boots; with socks no such principle suggests itself, and we cannot be sure, without the [Axiom of Choice], that there is a class consisting of one sock from each pair.

Gist of Idea

We can pick all the right or left boots, but socks need Choice to insure the representative class

Source

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

Book Reference

Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.126


A Reaction

A deservedly famous illustration of a rather tricky part of set theory.