I dont know why people still bother with Zeno's paradox of Achilles and TerrapinStation.

To get to where TP is at one point, takes less and less time for Achilles, until the distance between the two and the time to reach the point both reach zero.

You can only think about this in terms of Calculus.

The closer Achilles gets to TP, the less time it takes PROPORTIONALLY. Zeno assumed that it takes a non-proportional time. So by the time Achilles reaches TP, and the distance between them is zero, then the time elapsed to travel that distance is also zero.

IN other words, when the time elapsed between a prevous point in time to the time Achilles reaches TP is zero, the distance between the two of them is also zero.

Consider a sum of fractions: 1+1/2+1/4+1/8+1/16... which is the sum of all 1/2**n, for n= positive integers zero to infinity. There is a proof that proves that the sum is equal to 2. Don't ask me for the proof, because this was taught to us in grade 12, an immense amount of time before I forgot the proof. But I do live with the conviction that the proof exists!

Anyhow, if the distance halves between Achilles and TP and the time halves for achilles to reach the point where TP is, then somehow magically you can marry the two: (the sum of 2(**-n) and (Zenos paradox)), and there you go, bob is your uncle.

I am old-fashioned, and old-brained. If i remembered every proof and every thing I ever learned in school, then I would be crazier than I am not now.

The problem with adding fractions is that they don't necessarily represent space. Infinite space with finite length is the problem of Zeno.

I think most people miss the point of Zeno's motion paradox.
The introduction of an infinite series is not a solution, and would actually support his impossibility argument. While Achilles moves a distance x, the tortoise moves a distance y.
The underlined word is key, implying simultaneity. It was another poster (yrs ago) who called attention to the fact that the rate of motion was constant. Thus the time to overtake the tortoise was separation/(difference in speed). Zeno was demonstrating the nonsensical results from assuming space as a continuum.