Achilles and the Tortoise?

Zeno divided space up into an infinite number of finite lengths. The paradox is based upon Zeno's assumption that the sum of an infinite number of finite lengths would also be infinite. But that is not so. If you add up 1 + 1/2 + 1/4 + 1/8 + 1/16, etc. you would simply get 2 and not infinity. That an infinite number of finite lengths does not always add up to infinity had to wait until the development of the mathematics of infinite series to resolve the paradox. There are three possibilities for an infinite series: not converge to a finite number (which means it is unbounded or infinite), converge, or absolutely converge.

Of course Zeno didn't prove that motion doesn't exist. Everyone knows that who has ever watched a race. And, yes, Achilles actually was able to reach the tortoise, assuming he wanted to.

the ambiguity works thusly: assume 2 factors, A and B. the gap between them isn't important. with the intention to achieve B, you first ought to pass aspect C, which lies promptly between A and B. And with the intention to achieve C, you need to first pass aspect D, which lies promptly between A and C. in case you proceed this procedure again and again, not in any respect preventing, you locate that there is an unlimited style of factors you need to pass between A and B. see you later as you're vacationing from aspect to point, you would possibly want to not in any respect attain A and B. interior the case of Achilles and the Tortoise, the tortoise's distance establishes a clean aspect that Achilles ought to pass to achieve the tortoise. see you later because the time takes more advantageous than 0 seconds (which it does, because Achilles is operating at a finite speed), the tortoise has time to pass at the same time as Achilles catches up. you'll word that the Atomists (mutually with Democritus) got here about shorly after the Eleatic Monists (mutually with Zeno). by employing postulating a smallest-available unit of area, they were able to dodge such spatial paradoxes.