Well; the type of singularity might be relevant. It might be infinitely small; it might be infinitely dense; it might be infinitely massive; or any number of other infinitely things.

I suspect that singularities only exist in our mathematical treatment of things. They are a hindrance to the maths and usually cause the maths to break down at the singularity. You can't multiply by infinity and you can't divide by zero. Each case represents a singularity.