Thank you :^). I’ve always wondered about something else. Since dividing by zero is undefined, why not explore a case by case basis for division by zero? Case 1) x/0=0. Case 2) x/0=x. Case 3) x/0=infinity. Treat it sort of like a step function? Loosely speaking.
Obviously you are a better mathematician than I. I am a Physicist, with deep expertise in Materials Science. But compared to 99% of the population, Physicists are much closer to Mathematicians, than they are to the randomly selected individual. At MIT, I took every single math course that was offered for four years. But math is vast! Maybe even infinite :^). I particularly like probability and statistics.
You will probably get this one right, most folks do not. If you are on a number line, starting at zero, +1, +2, +3, +4 and so on to the right, and -1,-2,-3,-4…. to the left. Nothing fancy, just your standard number line. Now you have a fair coin, and each time you flip heads you take one step left, each time you flip tails you take one step right. If you were in Las Vegas, and you wanted to win, on what number should you place your bet after for the best odds of winning after 100 flips?