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Mathematics

The Banach-Tarski Paradox and Non-Measurable Sets

Quick fact

Quick Fact: The Banach-Tarski paradox shows that a solid ball can be cut into just five non-measurable pieces that can be reassembled into two equal-sized copies of the original ball.

Why this is interesting

Imagine slicing a basketball into a few pieces and then fitting those pieces back together to make two perfect basketballs, each the same size as the original. That’s exactly what the Banach-Tarski paradox claims is mathematically possible.