Zeno argues that motion is impossible because in order to get from one point to another, an object must first travel half the distance, then half the remaining distance, and so on, ad infinitum. Since there are an infinite number of distances to be traveled, the object can never actually reach its destination.

In reality, Achilles will eventually catch up to the tortoise, despite the paradox's argument that he cannot. Zeno's paradox is based on the assumption that an infinite number of smaller and smaller distances must be covered in order to reach a destination, but in reality, there is a smallest possible distance that can be traveled, such as the Planck length in physics.

Furthermore, the paradox assumes that time is infinitely divisible, which is also not true according to modern physics. When the actual physical laws are taken into account, the paradox can be resolved, and it becomes clear that Achilles can indeed catch the tortoise, given enough time.

Zeno's paradoxes continue to be interesting philosophical puzzles that raise questions about the nature of space, time, and motion, but their solutions lie in our understanding of modern science and mathematics, which provides a more accurate and realistic description of the world around us.