Popular culture gets Zeno’s paradox wrong again:
There’s a widespread impression that Zeno’s proposed problem is that after you reach the halfway point to your destination, you then have to go halfway to the remaining distance, and so on ad infinitum, so that you get closer and closer to your goal but never reach it.
But that’s not how the paradox goes. The problem is much worse. The paradox is that before you can get halfway to your destination, you have to get halfway to the halfway point, and so on ad infinitum, so that you can never even start moving. (Here’s Rose Wilder lane making the same mistake.)
Probably the mistake arose from someone conflating this paradox with another of Zeno’s paradox, the Achilles, in which the fastest runner gets closer and closer to catching up to the slowest runner.