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Copyright © 2011 Claremont Center for the Mathematical Sciences

**Claremont Mathematics Weekend**

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*Sponsored by Claremont Colleges*

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**January 30 - 31, 2016**

**Speaker:** **Asuman Aksoy****Title:** The Banach-Tarski Paradox**Abstract:**

The Banach-Tarski paradox states that a ball in 3-dimensional space may be decomposed and then reassembled by rigid motions as two balls of the same size as the original. At first glance, the paradox may seem preposterous since it strongly contradicts our intuition about the conservation of mass and volume. In this talk, rather than prove the Banach-Tarski decomposition, we give Vitali’s short proof of the existence of non-measurable sets. This helps us understand the paradox by showing that we cannot define volume for all subsets, but rather, only for some “good” subsets.