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
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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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some people (not many) would argue that everything past “countably infinite” is esoteric garbage. you have to toss out the real numbers to adopt this position though, and for almost all mathematicians that’s just impractical
i am basically pretty sympathetic to this view though. almost all real numbers are literally indescribable which is pretty sus. i think it’s totally reasonable to question whether they exist in any meaningful sense
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So far I agree with everything you've said..
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