After recently watching a couple of videos on supertasks and Achilles-turtle paradox, I'm curious - could Zeno's paradox be considered a "proof" that physically there has to be a smallest unit of length? Because at least physically, the paradox is resolved if we make that assumption.

I'm sure the above is nothing novel, but I want to know why exactly an argument like above may not work.

EDIT: In order to clarify this further, suppose I'm going towards a point 2 m away at 1 m/s. It'll take me 1 s to cover half the distance, or 1 m. Let's define a "step" as covering half of the remaining distance. So the 2nd step will mean covering 0.5 m in 0.5 s, and so on. The entire **process** of reaching my final destination is thus broken into infinitely many steps of 1 m, 1/2 m, 1/4 m, and so on. Of course, $\sum\_{1}^{\infty} \frac{1}{n} = 2$, but the number of steps is still infinity - there is no "last step". So how can a process without a last step be completed?

Apparently, one way to resolve this could be to say that the process actually has a finite number of steps. This means there is a physical limit to how many subdivisions of length one can make en route to the final destination. Hopefully this clears things up a bit.