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Graduate Pizza Seminar

Why can you double a ball but not a pizza

Fanxin Wu

Location:  Hill 701
Date & time: Friday, 26 January 2024 at 1:45PM - 3:00PM

One famous way to get rich quick with the axiom of choice is to buy a golden ball, double it a la Banach-Tarski, sell the first ball, and repeat this process. Other ways include using AC to predict lottery numbers, applying nonmeasurable trading strategy in stock market, etc. We will discuss the probably less known result that, while AC allows you to double a ball, it cannot double a pizza, which severely limits its practical value. Somewhat surprisingly, this is proven by using AC against itself. The key is a measure-theoretic property of group isolated by von Neumann, together with the fact that one can choose a random natural number uniformly.

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