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The Axiom of Choice is Wrong | The Everything Seminar: by Greg Muller This entry was posted on September 13, 2007
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When discussing the validity of the Axiom of Choice, the most common argument for not taking it as gospel is the Banach-Tarski paradox. Yet, this never particularly bothered me.
The argument against the Axiom of Choice which really hit a chord I first heard at the Olivetti Club, our graduate colloquium. It’s an extension of a basic logic puzzle, so let’s review that one first.
100 prisoners are placed in a line, facing forward so they can see everyone in front of them in line.
The warden will place either a black or white hat on each prisoner’s head, and then starting from the back of the line, he will ask