Well, this is the day of the week when I publish some old work of mine. Lately I seem to be scraping the bottom of the barrel. There's just not much material left in this category, but I have a metaphorical spatula, and there's still a little bit of crap way down at the bottom. After all, there's no sense throwing out a barrel until it's completely cleaned out.
A few years back during one of my futile attempts to get a degree in Computer Science, I took a class called Discrete Structures. (I never did find out what that term meant.) One of the assignments given to us was a workbook exercise that asked us to define a set with an infinite number of elements. Each element had to be a pair of values, and one of them (but only one) had to contain the same value for both elements. I did it wrong.
I defined the first element as containing zero and infinity, respectively, with each subsequent element incremented by +1 and -1, respectively. So the second element would be (1, (infinity-1)). I defined the final element to contain infinity and zero, respectively. Going backwards, it would be incremented by -1 and +1 respectively. Based on my logic, there would be an infinite number of elements in the set between the two endpoints, since that's how many it takes to get from 0 to infinity, counting by ones, and vice versa. At some theoretical midpoint between infinity and zero, the two values would be the same.
But as I said, this was wrong. The professor explained to me that you can subtract any finite value from infinity, and by definition you still have infinity. That makes sense, because otherwise the value could not have been infinite to begin with. But it makes equal sense that if one subtracts 1 from infinity an infinite number of times, one would get zero. After all, infinity minus infinity must equal zero.
I found this situation extremely interesting, because on the surface it would appear to be just another one of those insoluble philosophical conundrums, where you have two mutually exclusive answers, but neither can be excluded. (i.e. Could God make a rock so large he couldn't lift it?) But I also accept that the professor knew what he was talking about but couldn't explain it without getting into mathematics that were beyond me. I'm in awe of the fact that such things can be grasped by the human mind using higher mathematics, and before I die I will at least master Calculus. (Although it may take me 20 years.)