In mathematics

In mathematics, Zeno’s paradox is used to illustrate that “contrary to the evidence of one’s senses, motion is nothing but an illusion” (Zeno’s Paradoxes). The paradox goes as follows: Achilles and a tortoise are in a race together. The tortoise, of course, is slower than Achilles, so it is given a head start. Once the tortoise reaches one hundred meters, the race begins. Achilles sprints up to the on hundred meter mark and catches up to where the tortoise was. In that time, however, the tortoise moved further in the race, maybe ten meters. Now, Achilles has to again sprint to catch up with the tortoise. Sprinting another ten meters, he catches up to where the tortoise was. Again, in that time, the tortoise moved even further on in the race, maybe another meter. So Achilles has to sprint to catch up to where the tortoise was yet again. This keeps happening over and over again, and the distance between Achilles and the tortoise gets infinitely small, but not finite (Huggett). So does Achilles ever catch up with the tortoise? This is Zeno’s paradox. Obviously, he must catch up to the tortoise at some point. In the real world, Achilles would pass the tortoise and win the race. However, according to the paradox, traveling from his current position in the race to where the tortoise previously was—or from any location to any other location for that matter—would take Achilles an infinite amount of time.