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The Banach-Tarski Paradox

Thomas Schmidt
Foredrag for studerende
Fredag, 27 april, 2012, at 14:30-15:30, in Aud. D4 (1531-219)
One may state the famous Banach-Tarski Paradox as follows: Let $B$ be the unit ball of $\mathbb{R}^3$. Then there is a partition of $B$ into five disjoint pieces such that the pieces, after suitable rotations, can be reassembled into two identical copies of $B$. In other words, two people sharing a watermelon can each get a whole watermelon.

The proof of the Banach-Tarski Paradox is surprisingly elementary, requiring equal amounts of basic algebra, geometry and magic (in the guise of the axiom of choice). I will present the main ideas of the proof and skip most of the technical details. If at all, the talk will make sense for anyone who knows what a group is.
Kontaktperson: Søren Fuglede Jørgensen