Banach–Tarski paradox

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Can a baw be decomponed intae a finite nummer o pynt sets an reassemmled intae twa baws identical tae the oreeginal?

The Banach–Tarski paradox is a theorem in set-theoretic geometry, that states the follaein: Gien a solit baw in 3‑dimensional space, thare exists a decomposeetion o the baw intae a finite nummer o disjynt subsets, that can then be put back thegither in a different wey tae yield twa identical copies o the oreeginal baw.