Banach–Tarski paradox
The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: 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. Indeed, the reassembly process involves only moving the pieces around and rotating them, without changing their original shape. However, the pieces themselves are not "solids" in the traditional sense, but infinite scatterings of points. The reconstruction can work with as few as five pieces.
Banach–Tarski paradox - Wikipedia Jump to content From Wikipedia, the free encyclopedia Theorem in set-theoretic geometry For the book about the paradox, see The Banach–Tarski Paradox (book) . "Can a ball be decomposed into a finite number of point sets and reassembled into two balls identical to the original?" The Banach–Tarski paradox is a theorem in set-theoretic geometry that states the following: Given a solid ball in three-dimensional space , there exists a decomposition of the ball into a finite number of disjoint subsets that can be put back together in a different way to yield two ide
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