Zeno told a story about a race between Achilles and a tortoise. Achilles was, say, twice a fast as the tortoise. To help even the odds, the tortoise was given a 100 meter head start.
The race starts. By the time that Achilles runs 100 meters, the tortoise, who is half as fast as Achilles, has moved 50 meters ahead. When Achilles runs the next 50 meters, the tortoise has moved 25 meters ahead.
This has the appearance that Achilles will keep getting closer to the tortoise but never actually passing the tortoise because the tortoise is always a bit further ahead. No matter how small the distance between Achilles and the tortoise, there will be another smaller distance to travel all the way down to the infinitely small.
In Calculus 1, we learned that this was all bollocks and that Achilles whizzes past the tortoise at 200 meters.
Another problem in Calculus 1 dealt with a ladder. The ladder was leaning against a wall and someone was going to move the base of the ladder away from the wall at a speed of 1 foot per second. Our job was to calculate the speed of the top of the ladder when it hit the ground.
We came up with a formula and the result had us dividing something by zero. We checked with the instructor who surprised us by saying that we had the correct formula and the correct answer.
We knew that something was amiss because infinity doesn’t happen every day. We also knew that when a ladder slides down a wall, it does pack a wallop but not an infinite one.
The instructor put us out of our misery and explained. In a real-world demonstration of the ladder problem, the top of the ladder would leave the wall before hitting the ground. The formula wouldn’t apply and no infinities would mess up the ladder.
The moral of the story is: When someone starts talking about infinity, you know he’s fucking with you.