The Secret Magic of Dividing by Zero

Never divide by zero. We were all taught this in school, and in most everyday situations, it's good advice. It rarely makes sense to divide anything by zero, and if you try to ask Siri to do it, she will say you have no friends. But why exactly is dividing by zero such a bad idea? And are there cases where dividing by zero can be a good thing? If you weren't paying attention back in high school, a quick refresher can open your eyes to one of the many wonders of math.