Soon after I created thetalogy—which was then entirely based on the proof that theta divided by zero equals infinity—I would try to teach it to other people. I would start off by stating that any positive number (one, for example) divided by zero is infinity. But before I could get to proving this true, they would interrupt and say that you can’t divide by zero, that the answer is undefined. In my mind, I would get mad any time someone said this. The answer is not undefined, it’s clearly infinity!
It wasn’t until later when I made this realization: infinity is undefined. Not just because infinity isn’t allowed in math, but because the words basically mean the same thing. “Infinite” and “undefined” come from the same latin root “finis,” meaning limits, ends, or bounds. Thus, infinite and undefined both mean limitless, endless or unbounded. While the English word “undefined” doesn’t exactly have the same meaning as “infinite,” this realization made me feel a lot better about people saying that theta divided by zero is undefined. So next time someone tells me that one divided by zero is undefined, I’ll say, “Yes, one divided by zero is infinity!”
Now for the real question: why doesn’t math allow dividing by zero?
The answer is simple: algebra can’t work with infinity. In algebra, we make a lot of assumptions. We say that any number minus itself is zero, that all numbers are finite, that X equals X. But with infinity, these aren’t necessarily true.
In thetalogy, infinity is a set of infinite numbers. It’s impossible for us to find and compare infinite values, so they are grouped together in a single number, similar to theta being the set of finite numbers. But because of this, infinity does not always equal infinity. Infinity is greater than, less than, and equal to infinity. Therefore, subtracting infinity from both sides of an equation does not come out true. In fact, the equation was false from the beginning, it should have been something like a semi-inequality. The whole basis of algebra is ruined if you allow infinity, so mathematicians decided to call it undefined.