Hi. So I'm reading a physics book and I come across the following passage: Ok, up to this point I'm fairly confident I'm following along. But then they do the following: and I have no idea where this comes from. I am guessing here that [itex]p_i=\phi _i(q)[/itex] is only in some sufficiently small region and not the entire space, since they do not explicitly say anything in this regard, so that [itex]p_i-\phi _i[/itex] is not identically zero on the whole space, so I do not know where the above comes from. This is probably something really simple and I'm just being stupid, but any help is greatly appreciated.