The tortoise & Achilles one is solved with two sets of equations. Just graph that shit, and you find Achilles catches up with the tortoise at 10/9 units of time.
Ah, but Xeno never finishes graphing it, because he first has to graph the positions at time 5/9, but before that he must graph the positions at time 5/18, and so on. And since Xeno requires some finite time to graph any position, he never manages to complete the graph :]
Yeah, I was about to say this and you beat me to it. Zeno's problem was his inability to believe that you can add an infinite number of non-zero values together and get a finite result. Once you accept that you can add an infinite string of non-zero numbers together and get a finite answer, the paradox goes away.If I remember correctly, the problem that Zeno had was that he could not comprehend how one could sum an infinite sequence to arrive at a finite sum.
Yeah, I was about to say this and you beat me to it. Zeno's problem was his inability to believe that you can add an infinite number of non-zero values together and get a finite result. Once you accept that you can add an infinite string of non-zero numbers together and get a finite answer, the paradox goes away.
they don't like the idea that you do an infinite number of (sub)tasks, regardless of whether it takes finite time or not.
Maybe the problem is whether one should be allowed to subdivide a finite length into an infinite number of subdivisions.
But this is turning into a philosophical debate. I have no problem with Zeno's "paradox."