one of those weird things about math is that i “know basic calculus” in that i know the fundamental differential rules, but i feel like i don’t really “know calculus” in that i could not even begin to explain why they work
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and i’m not sure how easily i could purrove them, and even then i’m not sure i would find it illuminating conceptually
a lot of math you kinda just have to go “oh that just works out i guess” to keep yourself from losing your mind though. so whatever
like, i could purrove that Peano addition is commutative, but at that point the purroof is so mechanical i’m not really sure i could say i understand why it’s true. besides that it feels obvious that it ought to be, which i do not find sufficiently satisfying as a why