Point particles moving in continous space

[med17k]

does this statement make sense?
If Spacetime is continuous then a zero-dimensional classical particle would require infinite time to pass between 2 points in space because between any 2 points there is an infinite number of points but if classical particles have non zero space dimensions then they can move in the space from point to point . also if spacetime is discrete at the smallest scale then classical point particle can move ordinarily from point to point .

 

[mathman]

Your statement is a modified version of Zeno's paradox. It doesn't take an infinite time between points, since dividing up space also is also dividing up time, so the time is finite.

 

[K^2]

Look up convergence of infinite series. Wikipedia article titled "Convergent Series" might be a good place to start.