We have this interesting problem with black holes. What is a black hole? It is a region of space where you have mass that's confined to zero volume, which means that the density is infinitely large, which means we have no way of describing, really, what a black hole is!
As an astronomer, I get to ignore the details of the things that we don't understand. There's a lot of work that we can do on scales that we do understand, and there is actually a finite size that I can associate with a super massive black hole.