One of my favorite math quotes -- definitions are neither true nor false, they're either useful or not useful. So this misses it a bit. You can divide 0 by 0 f

One of my favorite math quotes -- definitions are neither true nor false, they're either useful or not useful. So this misses it a bit. You can divide 0 by 0 for example and it's 1. In fact you've probably already done it without thinking about it because it's so intuitive. f(x) = sum(x^n, n=0, 2) = x^2 + x + 1 f(0) = 0^0 + 0^1 + 0^2 = 1 and 0^0 = 0/0. It's a definition that's useful. If you remember your calculus you probably also remember that inf * 0 is also indeterminate but in measure theory you just define it to be 0 and move on. Also you can just straight up divide any number by 0 on the Riemann Sphere (the complex numbers adjoin infinity) and such a construction turns out to be good for modeling real world things. The floating point numbers adjoin infinity and make some definitions to make them work and it's good because again it's useful for the calculations people want to do. I get that it's not satisfying but division by 0 is whatever we want it to be because the answer isn't prescribed by the ring axioms. But if you make it too weird it won't by good for anything and every theorem and formula will have to account for your special case.