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Formal Proof of Banach-Tarski Paradox

Daniel de Rauglaudre 1, 2
2 PI.R2 - Design, study and implementation of languages for proofs and programs
Inria de Paris, CNRS - Centre National de la Recherche Scientifique, IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale, UPD7 - Université Paris Diderot - Paris 7
Abstract : 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.
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Submitted on : Friday, December 29, 2017 - 1:30:20 PM
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Daniel de Rauglaudre. Formal Proof of Banach-Tarski Paradox. Journal of Formalized Reasoning, ASDD-AlmaDL, 2017, 10 (1), pp.37-49. ⟨10.6092/issn.1972-5787/6927⟩. ⟨hal-01673378⟩

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