Banach-Tarski Paradox states that a ball in 3D space is equidecomposable with twice itself, i.e. we can break a ball into a finite number of pieces, and with these pieces, build two balls having the same size as the initial ball. This strange result is actually a Theorem which was proven in 1924 by Stefan Banach and Alfred Tarski using the Axiom of Choice.We present here a formal proof in Coq of this theorem.
@article{6927, title = {Formal Proof of Banach-Tarski Paradox}, journal = {Journal of Formalized Reasoning}, volume = {10}, year = {2017}, doi = {10.6092/issn.1972-5787/6927}, language = {EN}, url = {http://dml.mathdoc.fr/item/6927} }
de Rauglaudre, Daniel. Formal Proof of Banach-Tarski Paradox. Journal of Formalized Reasoning, Volume 10 (2017) . doi : 10.6092/issn.1972-5787/6927. http://gdmltest.u-ga.fr/item/6927/