In a fit of true geekiness, I was thinking about the saying “the sum is greater than it’s parts“ while taking a shower earlier. When I got back to my desk, I quickly scribbled the inequality using summations and some topos theory. I’m not too sure about my presentation but maybe I’ll come back to this and clear it up with a better presentation if it comes to me. Here’s what it looks like:
The inequality, in plain english, says that the sum of a series of numbers is greater than the sum of all those numbers. How this could possibly come about in mathematics, I have the faintest idea. I can’t think of any possible example that could prove this particular inequality. So I guess it’s one of those sayings that has no particular application to mathematics.
That’s it, end of procrastination. Still have a long day of reading ahead!
On second thought, maybe I shouldn’t use the disjoint union but rather instead. Maybe this is cleaner and simpler: