more from R Kaplan / E Kaplan

Single Idea 15717

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

Full Idea

The problem with the Axiom of Choice is that it allows an initiate (by an ingenious train of reasoning) to cut a golf ball into a finite number of pieces and put them together again to make a globe as big as the sun.

Gist of Idea

Using Choice, you can cut up a small ball and make an enormous one from the pieces


R Kaplan / E Kaplan (The Art of the Infinite [2003], 9)

Book Reference

Kaplan,R and Kaplan,E: 'The Art of the Infinite' [Penguin 2004], p.256

A Reaction

I'm not sure how this works (and I think it was proposed by the young Tarski), but it sounds like a real problem to me, for all the modern assumptions that Choice is fine.