So I always hear that the density of a black hole is infinite, because it's volume is zero. How can this be if, in mathematics, n/0 ≠ ∞? Would it be more correct to say a black hole's density is undefined or indeterminate? I also hear that some people say that a black hole's volume is "infinitely small" and they distinguish it from zero, if I'm not mistaking. What exactly would this mean? Is it's volume something more like 0.∞(point infinity)? Does that make mathematical sense? If not, then is there anything we can divide by to get infinity?