How do Zeno's paradoxes involve infinitely many divisions of distance?

Zeno of Elea’s paradoxes utilize the concept of infinite divisibility to challenge the possibility of motion and plurality. By arguing that space and distance are infinitely divisible, Zeno posited that any movement requires traversing an infinite number of sub-intervals, which he claimed was logically impossible.123

In his arguments against motion, such as the dichotomy paradox, Zeno asserted that to reach a destination, a body must first travel half the distance, then half of the remaining distance, and so on, ad infinitum. Similarly, in the Achilles paradox, he argued that Achilles could never overtake a tortoise because he must first reach the point where the tortoise previously was, by which time the tortoise has advanced further, creating a new interval to be crossed.21

These paradoxes highlight the tension between the physical experience of motion and the mathematical assumption that a finite distance can be divided into an infinite number of parts. While these problems remained challenging for centuries, they were eventually addressed through the development of calculus and the rigorous mathematical definition of limits, which allow for the summation of infinite series.2345