The Paradoxical Power of Axioms: Unraveling the Banach-Tarski Conundrum

Imagine a mathematician, armed with an infinitely sharp knife and a perfect sphere. She proceeds to slice and distribute the sphere into an infinite array of boxes, only to reassemble these pieces into five distinct sections. With a deft touch, she rotates and rearranges these sections, defying all logic, to form not one, but two identical, flawless spheres. How is this possible?