I've often seen black holes referred to as having a "singularity", which is described as a point of "infinite density", presumably due to the mass of the black hole occupying a point with zero volume (rather than having infinite mass in a finite volume).
Is there any evidence that this singularity is actually infinitely small, as opposed to just "extremely small"? For example, if it's the size of a quark (i'm just choosing a quark as an example of a "extremely small thing") then it's not infinitely small, it's just extremely small, and the density will just be extremely high rather than infinitely high.
I understand that due to the event horizon, we don't really know what's going on in there. But, since we know that the event horizon has a finite volume, why not assume that the black hole itself (or "the thing at the middle" - i'm not sure if the term "black hole" includes the event horizon or not) has a finite volume too?
Is the "infinite density" thing actually just a common misperception by writers?
EDIT - i just realised that a quark is a bad example of a "small thing" since i don't know if it's believed to have a volume. But you get the idea anyway, i hope.