Why does a ball bounce forever?
In short: Do bouncing balls keep bouncing forever? If not, does it have to do more with energy than velocity?
If energy is conserved, why do bouncing balls, pendulums, and other cyclic systems eventually stop moving? The energy doesn’t disappear but rather it is transferred to the surroundings, where it is unavailable to keep the cycle going. The result is that most objects moving in cycles eventually move less and less and then finally stop.
But that wouldn’t make sense mathematically: although the limit converges to zero, it doesn’t fully ever approach it. Do the mathematical laws break down at the micro physical level much like they do in general relativity? Does the ball keep bouncing up and down but reaching some height in space $epsilon > 0$?