In my current physics book one line reads:
"The laws of mechanics are Galilean invariant.",
"No mechanical experiment can be used to tell whether an inertial frame is moving or at rest (with respect to any other frame).".
I understand that you cannot tell whether you are moving with respect to something else or whether that something else is moving with respect to you, or that you cannot tell whether you are being accelerated with respect to another frame or vice versa. But does the corollary basically imply that since you can take both reference frames at rest and have the other move with respect to your chosen frame, that either can be moving with respect to the other?