Banach-Tarski paradox

proper noun

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.

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Meanings

proper noun
  1. mathematicsA 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.

Origin

Named after Polish mathematicians Stefan Banach and Alfred Tarski.

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Translations

French paradoxe de Banach-Tarski
  • paradoxe de Banach-TarskiTranslations
German Banach-Tarski-Paradoxon
  • Banach-Tarski-ParadoxonTranslations
Hungarian Banach–Tarski-paradoxon
  • Banach–Tarski-paradoxonTranslations
Italian paradosso di Banach-Tarski
  • paradosso di Banach-TarskiTranslations
Polish paradoks Banacha-Tarskiego
  • paradoks Banacha-TarskiegoTranslations
Cite this entry
APA

Banach-Tarski paradox. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Banach-Tarski%20paradox

MLA

“Banach-Tarski paradox.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Banach-Tarski%20paradox. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Banach-Tarski paradox,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Banach-Tarski%20paradox.

Source: Banach-Tarski paradox on Wiktionary, CC BY-SA 4.0.