In ancient Greece, philosopher Zeno of Elea (c. 450 BCE) challenged conventional belief, arguing that in a race, achilles would never catch up with the tortoise, so long as the latter was given a head start. Of all his notable paradoxes, this paradox might well be most synonymous to his name. A paradox, is an assertion, which seems to be self-contradictory, yet is nonetheless correct (or synchronously incorrect).
In this paradox, the turtle is given a 10 meter head start. Hence, to reach the tortoise and outdistance him, Achilles would first have to cover the distance at which the tortoise began. During this process, the tortoise, would have moved further, let us assume this to be 1 meter. In order to reach the tortoise now, Achilles would have to cover that distance, yet in doing so, the tortoise would have further ambled forward, i.e. 10 centimeters. This logical progression would go on ad infinitum.
Zeno had conjectured this paradox, in defense of his mentor Parmenides, whom contended that motion was a mere illusion. Yet, despite being fallacious, Zeno’s paradox did influence key mathematical concepts, such as infinite series, and proved that finite series could be infinitely divisible.