How do Zeno’s paradoxes connect endless division with the problem of motion?

Zeno of Elea utilized his paradoxes to argue that motion is an illusion, relying on the premise that space and time are infinitely divisible. By challenging the commonsense belief in motion, he sought to support the Parmenidean view that reality is a single, unchanging entity.123

In the famous paradox of Achilles and the tortoise, Zeno argued that for Achilles to overtake the tortoise, he must first reach the point where the tortoise started, then the next point, and so on. Because the distance is infinitely divisible, Achilles must traverse an infinite number of intervals to catch the tortoise. Zeno’s logic implies that because an infinite number of tasks cannot be completed in a finite time, motion is impossible.142

Mathematically, this problem involves the sum of an infinite series, such as a geometric series. While Zeno viewed this as a contradiction, modern mathematics resolves it through the concept of a limit, where an infinite sequence of subdivisions can converge to a finite sum.526