> The claim of the proof is that I=F(0)+F(π) is simultaneously positive and arbitrarily small, which is not possible for a fixed number, but totally possible if

> The claim of the proof is that I=F(0)+F(π) is simultaneously positive and arbitrarily small, which is not possible for a fixed number, but totally possible if you see I as a sequence indexed by n. This is not possible because I_n must be an integer for every n.