Can Singularities Really Exist?

I’ve often heard that there is a singularity at the center of black holes. And I understand that a singularity as being a place that is infinately small.

How can anything actually become infinitely small? I can understand becoming small beyond comprehension, but how do you reach infinitely small when infinity can not be reached?

Also, why wouldn’t the small between atomic particles in a black hole be limited to something like planks length?

That last line was suppose to say space instead of small.

Welcome to the boards LiquidAmber!

I’m no expert, but I’m guessing that the singularities become that small by the immense pressure of the black hole.
I’m also guessing that in reality, there is a point that could maybe be measured possibly, but I think the point of a singularity is that it is so small it is radically beyond our measurement.

A singularity is by definition a place in which our current physics cannot be applied. Saying what a black hole is becomes very difficult. But I don’t think that black holes are usually referred to as infinitely small. Can you give a cite of a place that uses that term?