mad props to the lagrange inversion theorem https://en.wikipedia.org/wiki/Lagrange_inversion_theorem
ok so, the classical proof that
root(2) involves deriving a contradiction from the assumption that root(2) is rational.
however, there is an argument to be made that there is a difference between a number being [not rational], and actually provably belonging to the class of irrational numbers, i.e. quantifiably different in some way from every rational number.
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