1) The ball stops bouncing in a finite amount of time. 2) The ball bounces an infinite number of times. 3) This is not a contradiction, no more than the idea

1) The ball stops bouncing in a finite amount of time. 2) The ball bounces an infinite number of times. 3) This is not a contradiction, no more than the idea that a projectile passes through an infinite number of spatial points in finite time. Please go and read about geometric series and Zeno's paradox on wikipedia, as another commenter has already suggested.