system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5:How do we "know" black holes are infinitely small with infinite density? Why can't they just be extremely small and extremely dense so the math isn't ridiculous?

Why can't a black hole simply be massive and dense enough to have an escape velocity higher than C without being infinitely small and infinitely dense?
gpt
With what little we *know* about black holes, the math shows them to be essentially infinitely small and infinitely dense.  Of course, intuitively, that makes no sense to our brains, which are used to seeing matter take up space and have defined density.  This means that there are two broad possibilities:

* The math we're using is wrong, and there's an undiscovered way for the math to more accurately map reality.

* Black holes really do approach infinity; the math is correct, and we need to update our understanding of the universe to include this fact.