A convergent sequence doesn't have to be a digit expansion and so might not have the nice property that "if it's just repeating, it's rational, otherwise irrati

A convergent sequence doesn't have to be a digit expansion and so might not have the nice property that "if it's just repeating, it's rational, otherwise irrational." Furthermore, it wasn't proven until the 18th century that Pi was irrational (https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrationa...). To this day, it is unproven that pi+e is irrational, yet the decimal expansion is easy to compute (and you'd be a fool to bet on it being rational).