Your are referring to a variation on
Zeno’s Paradox of the Tortoise and Achilles , circa 350 BCE. Zeno's Paradox essentially argued that motion was not actually possible.
The paradox is fairly easily disprovable:
Quote:
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Now the resolution to Zeno's Paradox is easy. Obviously, it will take me some fixed time to cross half the distance to the other side of the room, say 2 seconds. How long will it take to cross half the remaining distance? Half as long – only 1 second. Covering half of the remaining distance (an eighth of the total) will take only half a second. And so one. And once I have covered all the infinitely many sub-distances and added up all the time it took to traverse them? Only 4 seconds, and here I am, on the other side of the room after all.
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I had a math teacher who used Zeno's Paradox to define the terms "for all intents and purposes." He proposed lining up all the boys on one side the room and all the girls on the other. If each line moved half way to the other and then half way again and so forth, they would at least per Zeno, never meet. They would however very quickly get close enough "for all intents and purposes."