In the tortoise at some point. In

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. Knowing that the tortoise is slower than Achilles, the tortoise is given a head start. The race begins once the tortoise reaches one hundred feet. Achilles eventually reaches the point that the tortoise originally was when given the head start, but in that time, the tortoise moved further in the race. Now ten feet ahead of him, Achilles sprints to catch up to the tortoise’s current position. In that time, however, the tortoise moved one foot further in the race. Forced to catch up to the tortoise, Achilles is forced to sprint to where the tortoise was yet again. This process keeps happening over and over again, with Achilles continuously sprinting to catch up to the tortoise and the tortoise inching forward slowly but gradually.

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The distance between the two runners 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.