Deep in the foundations of mathematics lies a simple axiom that produces one of the strangest paradoxes in history. And a direct consequence of this axiom is that not only are there mathematical sets with zero volume but there are also sets for which it is impossible to assign a meaningful sense of volume.
Can all mathematical sets be assigned a meaningful volume? In this video, I will show you how this simple question plays a crucial role in the Banach-Tarski Paradox and use it to motivate the study of a fascinating subject known as Measure Theory.
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Music by Vincent Rubinetti
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