The Achilles' Paradox is meant to convey the idea of infinite divisibility. Zeno was trying to show that motion and change are an illusion, and that there is no such thing as motion because in order to move from one point to another, an infinite number of smaller motions must occur. In the paradox, the idea is that Achilles can never reach the Tortoise because for each point in time that Achilles closes the gap between them, the Tortoise will have moved a little further, thus creating a new gap for Achilles to close. This creates an infinite regress, and therefore, the idea is that motion is an illusion and does not truly exist.
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