3282: Trick Play

Trick Play

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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.

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Explanation

This is one of 44 incomplete explanations: This page was created by the math department, which is salty after last game. Don't remove this notice too soon. If you can fix this issue, edit the page!

The Banach–Tarski paradox is a theorem in set-theory geometry saying that a solid ball in three-dimensional space can be taken apart into a finite number of disjoint subsets, which can then be reassembled into two solid balls that are each the same size as the original. The subsets, which can number as few as five, aren't solid objects, but rather infinite collections of points. Here the soccer team of (presumably) a college math department has done this with the soccer ball during a game, starting with one ball, using the B-T paradox to make it into two, attacking the opponent's goal with both at once, and scoring with one of them. This would be difficult to do with a real soccer 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.

Transcript

This is one of 30 incomplete transcripts: This transcript was created by William Shanks, who continues to calculate PI years later, from beyond the grave. Don't remove this notice too soon. If you can fix this issue, edit the transcript!

[A diagram of a little more than half of a soccer 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 (movement) are drawn between some of them. In the middle of the diagram, an O player 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.]

[Caption below the panel:]

The math department team's opponents hate it when Banach passes to Tarski.

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Discussion

Ive been here before the comments but never before even a explanation, or even a transcript! Ill do a good deed and add the transcript rq 163.120.65.183 17:34, 7 August 2026 (UTC)
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