Where's the limit?

In the Dichotomy Paradox, Zeno argued that a runner can never reach the finish line on a straight track. The logic is simple. The runner must first cover half the distance to the goal. Once there, he must still cover half of what remains. After that, he must cover half of the new remainder, and so on, and so on. At each step, some distance remains. In Zeno’s telling, the runner is never able to reach the finish line. But while Zeno’s runner never arrives, the real world does have real limits, and we are moving steadily closer to physical supply hitting effective tank bottom.