Another good point, you could make a good case for the mass in a black hole being a point and hence infinite density existing, there are alot of problems with black holes because we know so little of what goes on inside them. So you might well be right, but i could argue that the mass is not a point it is merely forever shrinking, hence has a fixed volume at any point in time and hence a finite density...
I don't know why but i'm wary of infinites, it may well be just because i don't like the idea in exactly the same way i didn't like the idea of quantum mechanics when i was first introduced to it, its just doesn't feel right somehow, of course i may be well off, and black-holes and maybe many more phenomena show examples of infinite values.