The Banach–Tarski paradox

Abstract

for 28 Mar 2013 In 1924, Banach and Tarski proved that any bounded solid region in 3-space can be decomposed into finitely many pieces that can be rearranged using Euclidean isometries to produce any other bounded solid region desired. As it is often put, "a pea can be chopped up and reassembled to produce the sun." I will present this paradoxical result and discuss the extent to which the Axiom of Choice can be blamed for it.