more from Brian Clegg

Single Idea 10879

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

Full Idea

Axiom of Choice: For every set we can provide a mechanism for choosing one member of any non-empty subset of the set.

Gist of Idea

Choice: For every set a mechanism will choose one member of any non-empty subset


Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)

Book Reference

Clegg,Brian: 'Infinity' [Robinson 2003], p.206

A Reaction

This axiom is unusual because it makes the bold claim that such a 'mechanism' can always be found. Cohen showed that this axiom is separate. The tricky bit is choosing from an infinite subset.