What is the solution to Zenos paradoxes?
In about 445 B.C., the Greek philosopher Zeno of Elea offered several arguments that led to conclusions contradicting what we all know from our physical experience. The paradoxes had a dramatic impact upon the later development of mathematics, science, and philosophy. His most familiar paradox, the paradox of Achilles and the Tortoise, involves the fast-running Achilles and the slow-crawling tortoise. The tortoise has a head start. If Achilles hopes to overtake the tortoise, he must at least run to where the tortoise is, but by the time he arrives there, the tortoise has crawled to a new place. So, Achilles must run to the new place; but of course the tortoise isn’t there, having crawled on to yet another place, and so on forever. Therefore, Zeno argues, good reasoning shows that fast runners never can catch slow ones. So much the worse for good reasoning. Notice that Zeno’s reasoning rests on the assumption that time is continuous, that is, that time can be divided into infinitely man
