Singularity in a black hole

Question

This might be a naive question, but how can an object such as a black hole singularity have infinite density but finite mass? (For example, we can approximate the mass of a black hole based on Kepler's Laws and use info from surrounding movements of stars to determine the central mass, but the black hole, excluding the event horizon, has infinite density.)

Answer 1

The simple way to think about it is the following limit: $$\rho = \lim_{V\to0}\frac{M}{V}$$

As $V\to0$, $\rho\to\infty$ while $M$ remains constant.