This is with regards to the principle of least action. I understand that an action is a functional (a function where functions have values assigned to them, I believe?) When trying to figure this out, I understood minimising as finding the true path of the principle of least action. But that does not make complete sense - if the true path is the path where the action is minimised MOST, what about the other paths? They can be minimised as well, right? S (trial) = S (true ) + some terms l x(t)^2 l according to my lecturer in classical mechanics. So if S (trial) is S (true), than those terms on the far right need to disappear, right? But what if they can't disappear because we have a false path? How (or can we) minimize the action still? As you can see, I am very confused about the meaning of "minimising" the action. Mathematical explanations would be helpful as much as conceptual ones.