Asuman Aksoy's Abstract

 

Claremont Mathematics Weekend

 

Sponsored by Claremont Colleges

 

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.