Just learned about the Banach-Tarski paradox and I'm mad
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the pieces in the banach-tarski decomposition don't exist in any remotely meaningful sense. they're non-measurable among other things, which means they "don't have a volume / weight." it's esoteric axiom of choice garbage from a "real-world" perspective
the "most meaningful" part of banach-tarski is a group theory thing that is sort of like how you can take the integers and divide them into the even and odd integers which "have the same size" as the integers. the axiom-of-choice garbage is how to relate this to balls
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I think "counting infinites" is just dumb but I don't know if anyone else is with me on this
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Yeah, what it really says is 1) that you can do a mapping from one ball to two balls, which is obvious as they are both uncountable and 2) you can do 1) in a clever way, but so what
Not really a paradox, just a slight of hand.
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In my experience, things that defy logic usually don't actually.