John Platko wrote:I'm pretty sure I understand. I also understand that while limits are the modern way of teaching integrals, it is not the only way to understand them.
But, if you see some obvious error that I'm making, why not just spell it out clearly. My question is clear enough.
Newton's laws
describe (certain aspects of) behavior, they do not prescribe it. Specifically, it describes a way for one to calculate forces, masses, or accelerations(velocity(position)) if you happen to have made some measurements.
For example, if you have measured the mass and acceleration of an object, you can calculate the force acting on that object. Furthermore the accuracy of your calculation is only as good as that of your measurements.
It is unwarranted to draw any conclusions about ultimate reality (i.e. your weird assertion about infinite velocity/energy changes) simply because the method of calculation is based on a continuous model of the universe.
Your golf ball question has been answered. Yes, Newton's Laws have been shown to be incomplete for high velocities and small scales. They are still applicable and accurate enough to fly a robot to Saturn and land a probe on Titan.