The ancient Greeks never <quite> got to calculus though they did get 'close enough' IMO. And yes, the arrow will never reach its target because there are infinite 'sections' of distance it must travel is the basis of the concept of limits and asymptotic lines: places one cannot get to but they would be the correct answer if one could go there. But again, when applied to things like moving objects and trying to use these mathematical concepts where they do not belong or apply is, again, mental masturbation IMO.

y = 1/x As x tends toward infinity (works the other way too, as x tends toward zero), what happens to y. The classic example of limits and asymptopes. You cannot divide by infinity but the closer you get, as x gets bigger, the closer y gets to zero. Hence the limit of the function is zero- a place you cannot get to but you are 'tending toward' that value. And so y 'tends' toward zero. The concept simply does not apply to a moving object and the travel over distance.

But the world is full of miss- applications like that. I always thought Schrödinger's cat was ridiculous, as I think modern quantum physics having electrons disappear and reappear randomly is too.

Brian

Now you've gone all calculus on us. I think

"If Achilles is to run from point A to B, he must first travel half the distance, then half again, and so on. Taking the distance from A to B as one, the distance Achilles must travel is the series 1/2 + 1/4 + 1/8...... Because there is an infinity of terms in this series, Achilles can never reach his goal."