The Point of the Banach-Tarski Theorem

Re:The Point of the Banach-Tarski Theorem by smcl on Monday January 23, 2023 @06:21AM (#34487569)

I did get a chuckle at that, like the running joke about how a monad is “just a monoid in the category of endofunctors”. To be fair, you could delete the “R^3” part and the explanation can still be understood.

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Re:The Point of the Banach-Tarski Theorem by yellowapple on Monday January 23, 2023 @11:39AM (#34491123)

Hell, deleting the 𝕽³ part probably would've made it clearer: "ball" already implies 3D space for me, whereas seeing that qualified with some janky-ass medieval R had me second-guessing about it being one of those math quirks involving non-euclidean space or imaginary-number dimensions or whatever else mathematicians come up with in their efforts to compute the passcode on the Gates of Hell.

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Re:The Point of the Banach-Tarski Theorem by smcl on Monday January 23, 2023 @12:29PM (#34491988)

Yeah I feel you - I think these things come so naturally to mathematicians that it's hard for them to conceive of the idea that people like you and I exist :)

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