Originally Posted by **topsquark**

Well, let's not be too hasty about that. Quantum field theory seems to imply that there is a "cut-off" level in the structure of space-time. i.e. It appears that space-time has a non-continuous structure at extremely small scales. (This is, at least, one of the more reasonable ways to remove the ultraviolet divergent integrals.)

For a more basic example, consider an object falling into water. The speed function is certainly continuous, but the acceleration function has a discontinuity at the water-air interface.

-Dan