Infinity shapeshifter vs. Banach-Tarski paradox

Take on solid ball, cut it into a couple of pieces and rearrange those pieces back together into two solid balls of exactly the same size as the original ball. Impossible? Not in mathematics!
Recently Vsauce did a brilliant video on this so-called Banach-Tarski paradox: https://youtu.be/s86-Z-CbaHA
In this prequel to the Vsauce video the Mathologer takes you on a whirlwind tour of mathematical infinities off the beaten track. At the end of it you'll be able to shapeshift any solid into any other solid. At the same time you'll be able to appreciate like a mathematician what's really amazing about the Banach-Tarski paradox.

Enjoy :)

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