things that make me rationally angry (but are also really cool at the same time)

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things that make me rationally angry (but are also really cool at the same time)
#1
things that make me rationally angry (but are also really cool at the same time)
godel's incompleteness theorems

church 'n' turing's uncomputability proofs

the heisenberg uncertainty principle

non-integrable functions that clearly have a sensible integral (like 1/ln(x))
(similarly, unsolvable dif. eq. that have a simple and sensible numerical solution)

the fact that there are probably irrational numbers that are impossible to describe other than by listing their infinitely many digits

long addition
#2
RE: things that make me rationally angry (but are also really cool at the same time)
Regarding integrability, it's fairly common practice to just define non-elementary functions, like for that case, li(x)