Point particles moving in continous space

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

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