>>38
we know that black holes have entropy (http://en.wikipedia.org/wiki/Black_hole_thermodynamics), and that the maximal entropy of a region scales with the surface area (http://en.wikipedia.org/wiki/Holographic_principle). if the volume of a non-rotating black hole is 0, then the surface area is 0. if the surface area is 0, then the maximal entropy of the black hole is 0. rotating black holes could have 0 volume but nonzero surface area, but not large enough surface area for their entropy.

tl;dr infinite compression breaks thermodynamics.

If the universe were finite, gravity would make an example of it.
Says Hawking.