system
Given the following post, respond as if you're commenting on Reddit:
human
If imaginary numbers were created to solve the otherwise unsolveable problem of roots of negative numbers then why dont we create other imaginary numbers to solve other unsolveable problems like x/0?
gpt
First, imaginary numbers weren't created to solve the problems of roots of negative numbers. People were perfectly fine with negative numbers not having roots. Rather it was attempting to solve the seemingly unrelated problem of roots of cubic equations that roots of negative numbers came into play. It basically forced mathematicians to realize that there was something there, though resistance to these numbers remained, with mathematicians calling them "useless" and "imaginary." Nonetheless, they opened the way to expanding our understanding of math.

Unlike imaginary numbers, most attempts to find something to make things like x/0 work tend to break everything else. There are mathematical frameworks that do make sense of this, but tend to involve making sacrifices by way of getting rid of other mathematical concepts in order to prevent things like x/0 from just breaking everything.

In your typical, day-to-day math, that sacrifice is generally not worth it, so we leave x/0 as being undefined.