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Journal Articles Journal of Formalized Reasoning Year : 2017

Formal Proof of Banach-Tarski Paradox

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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Dates and versions

hal-01673378 , version 1 (29-12-2017)

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Daniel de Rauglaudre. Formal Proof of Banach-Tarski Paradox. Journal of Formalized Reasoning, 2017, 10 (1), pp.37-49. ⟨10.6092/issn.1972-5787/6927⟩. ⟨hal-01673378⟩
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