And you say, OK, fine. You won that round. Let me make it even tighter. Maybe instead of saying within 0.5, I want to get within 0.05. And then you'd have to do this exercise again and find another range. And in order for this to be true, you have to be able to do this for any range that they give you. For any range around L that they give you, you have to be able to get f of x within that range by finding a range around c that as long as x is that range around c, f of x is going to sit within that range.