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| Trick Play |
 Title text: I've been trying to find out whether the Laws of the Game take the axiom of choice or not, but FIFA officials keep blocking my number. |
Explanation
The Banach–Tarski paradox is a theorem in set-theoretic geometry saying that a solid three-dimensional object — in this case, a sports ball — can be taken apart into several pieces (usually five) and those pieces can then be reassembled into two identical copies of the original object. The paradox has been proven true for any object at the theoretical level, but is difficult to replicate in real life because it requires the objects to be made of infinite collections of points, rather than a finite number of atoms. The paradox has been mentioned before in 804: Pumpkin Carving.
Here the football (soccer) team of (presumably) a college math department has done this with the football ball during a game, starting with one ball, then Stefan Banach and Alfred Tarski use their namesake paradox to make it into two balls, attacking the opponent's goal with both at once, and scoring with one of them. This would be difficult to do with a real ball.[citation needed]
The title text refers to the axiom of choice, an axiom of set theory that says that given an infinite number of non-empty sets, it's possible to choose one element from each of these sets. The axiom of choice, which is not accepted in all set-theoretic work, is necessary to prove the Banach–Tarski paradox. FIFA is the top-level institution governing football, including implementing the Laws of the Game, the rules laying out how the game is played. It's implied that Randall's phone number has been blocked due to calling the organisation too many times with math questions.
Transcript
- [A diagram of a little more than half of a football field is shown. Multiple individuals are on the field. The two teams are represented as O's and X's, and there's a goal at the top of the diagram. Arrows (passes) and dotted lines (dribbles) are drawn between some of them. In the middle of the diagram, an O player simulataneously passes to two other players, one diagonally up to the left, the other diagonally up to the right. Each of those receiving players kicks their ball towards the goal. There's an X goalie near where the left ball enters the goal area, but the right ball is unopposed as it goes into the goal.]
- [Caption below the panel:]
- The math department team's opponents hate it when Banach passes to Tarski.
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