Infinity

For quite some time, I was confused by – what I thought was - a simple question that involved limits, infinity, and asymptotes. In Algebra, everyone learned that when you graph the function y = 1 / x, you have a result with asymptotes, or sections where the graph appears to be approaching zero from different directions, but never really reaches there…or does it?

Everyone has probably also been over the fact that dividing 1 by half, then by half again, over and over the result approaches zero, but shouldn’t ever really get to zero. If you divide it in half an infinite number of times, you get so close to zero, you are practically at zero.

Which then leads to my confusion: if you are driving towards an oxygen molecule a mile away, you get closer and closer and closer, but at what point can you not get any closer? If you think of it, no matter how close the car gets to that oxygen molecule without touching it, there is an infinitely small distance that can be covered. So the car goes half the distance. Again, there is still more space that can be covered. Either the car is touching the molecule or not, right? Is it a truly this dichotomous? Is it so digital that there really is no such thing as analog? Does a baseball slow down when it is hit after being pitched, or does it instantaneously go from 100 mph one direction to 120 mph in another? How does that work?

One of the things I remember from physics is that the car and the oxygen molecule would never really touch, but the molecules on an atomic level would be close. My friend and I joked that when you kiss a girl, you really aren’t touching her because the molecules would be repelling each other. Although it’s funny, it’s still a serious question for which I want an answer I understand.