prove that sin(1) (one radian) is irrational.
Hint start with taylor series expansion
you first need this basic and simple fact about alternating series that if then
now suppose for some let
thus is an integer. i'll show that this is false, i.e. cannot be an integer: using the MacLaurine expansion of we have:
it's clear by that we also have:
therefore and so is not an integer. Q.E.D.