3 ms·

What is the type of x and y? If it's ℝ, why wouldn't x / y be of type *ℝ (hyperreals)? I'm just your average programmer, not into abstract logic stuff, but got

• hansvm 1y ago
  The hyperreals don't fix the x/0 or 0/0 problems. Infinitesimals have a well-defined division and take the place of a lot of uses of 0 in the reals, but the hyperreals still have a 0, and the same problem posed in their comment exists when you consider division on the hyperreals as well. I'm also curious what they intended, but there aren't many options: 1. The question is ill-posed. The input types are too broad. 2. You must extend ℝ with at least one additional point representing the result. Every choice is bad for a number of reasons (e.g., you no longer have multiplicative inverses and might not even have well-defined addition or subtraction on the resulting set). Some are easier to work with than others. A dedicated `undefined` value is usually easy enough to work with, though sometimes a single "infinity" isn't terrible (if you consider negative infinities it gets more terrible). 3. You arbitrarily choose some real-valued result. Basically every theorem or application considering division now doesn't have to special-case zero (because x/0 is defined) but still has to special-case zero (because every choice is wrong for most use cases), leading to no real improvements.
  • magicalhippo 1y ago
    Good point, forgot about 0/0.