[godelski]

> Are black holes real?

Yes

> Do they have singularities?

¯\_(ツ)_/¯

The math leads us there but I don't think anyone is particularly happy about it.

> Is pi “real”?

¯\_(ツ)_/¯

> Is the plank constant?

¯\_(ツ)_/¯

Fuck man, I can't tell you if a quark is real. I'm also not aware of anyone who can. The best we got is our interpretation that the model being indistinguishable from the real thing might as well be the real thing. Metaphysics and metamathematics are mind bending areas that require a deep understanding of the non-meta concepts first.

But given all you've said, I highly suggest looking into the various set theories I mentioned previously. Specifically start with Finite ZF set theory and Peano Arithmetic, where you'll find you can indeed operate on such concepts as pi without infinities.