Zeno’s paradox origins from the concept that a single line segment will have an infinite number of points. The paradox is the following.
If Achilles tries to catch a tortoise that is slightly ahead of him, he cannot reach the tortoise at a finite time. By the time Achilles reaches the initial position of the tortoise, the tortoise might have already moved ahead. He needs to move infinitely, because as Achilles moves closer to tortoise, the tortoise would have moved slightly ahead, though at a very very miniscule level. So, where does this infinity end? Does it end at all? Where do we keep a pull stop?
Modern Implication: Think about calculating the area of a finite circle using triangles. You keep adding triangles inside the circle and fill most of the space of the circle. As you keep increasing the triangles, you might decrease the extra space but could never fill the whole circle with triangles. Infinite triangles in a finite circle! That is why we stick to approximations.
This approximation is exactly what we use in integration (calculus), which Newton and Leibniz discovered.
