Anti-Inductive Phenomena and Baire Category

I've mentioned on occasion that markets are anti-inductive. There is a connection between anti-inductive phenomena and one of the more apparently-useless branches of mathematics: point-set topology.

You can think of real numbers as sequences of digits. It turns out that the set of real numbers corresponding to anti-inductive sequences is a dense G_δ point set, i.e., the complement of a set of first category.

Maybe someday we'll also find a use for the Banach–Tarski paradox.