Banach-Tarski paradox

== English == === Etymology === Named after Polish mathematicians Stefan Banach and Alfred Tarski. === Proper noun === Banach-Tarski paradox (mathematics) A theorem in set-theoretic geometry, which states that given a solid ball in three‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball.