Fair enough. I do see how you could think that it's intuitive. I've even used your explanation when I'm teaching. Although I can't help but think there's some s

Fair enough. I do see how you could think that it's intuitive. I've even used your explanation when I'm teaching. Although I can't help but think there's some sort of circularity going on here, at least for me. My intuition on the subject is shaped by my knowledge of the theorem, and the functions that I tend to work with.