Or rephrased: is instantaneous velocity real? Are limits real, or just a mathematical invention? Well, I think instantaneous velocity is real, and I think I ha

Or rephrased: is instantaneous velocity real? Are limits real, or just a mathematical invention? Well, I think instantaneous velocity is real, and I think I have a convincing argument. Imagine you have a piece of gum stuck to your bike tire. As your tire spins, the piece of gum spins with it, and its velocity is constantly changing. But when the piece of gum flies off your tire, it flies off in a straight line, following the instantaneous velocity at the moment of separation. Seeing as the gum can fly off in a straight line, its instantaneous velocity at that moment must be well-defined.