/sci/ - Science & Math

>What's x at y = 0?
>What's the limit?
Limit = value that a function approaches =/= what it is

So let me get this straight.

Math is supposed to be this set of rules that always apply equally in every case, and if it fails to apply in a specific case then the rule was just lucky to apply in the other handful of cases and is scrapped aside. For an example, imaginary numbers and their application literally everywhere and no matter how hard you try to find a flaw in them, you can't because they function in every single case without exceptions, therefor, they exist and there's nothing you can do about it.

Fine. So what about division by zero then? How come we pretend this didn't happen and just reflexively go "undefined lmao next" every time it pops up, fully ignoring the fact that it keeps popping up everywhere but no one has any idea what's happening? Is this a problem we're yet to solve and finally find a concrete solution to x/0 that applies everywhere without exceptions or different infinities popping up, or is there no actual solution which means that the entire infrastructure of math is actually flawed and we should start anew?

In both cases this seems like a problem that must be handled NOW, in fact the most important problem of modern math which is probably bottlenecking our next major step in scientific development much like the refusal to use negative numbers and even imaginary numbers were for quite some time. So why the fuck is literally no one looking into it and trying to dig out a solution in the same way there's a legion of PhDs trying to solve the Riemann Hypothesis?