Do black hole singularities actually merge?

new questioner here so please be gentle.

Do the singularities of merging black holes actually merge together? I mean there are 2 infinitely small objects (singularities) that are trying to find each other but for them to merge they have to join at the EXACT same point in space. I know they can get close, but to expect them to align perfectly with zero tolerance seems impossible.

• I think the broad stroke of the answer is: it's the event horizons that merge, not (necessarily) the singularities. – zibadawa timmy Feb 18 '16 at 0:15
• I rather like this question cause it's both, simple and at the same time, probably impossible to answer. A problem lies in defining what a singularity is. See physics.stackexchange.com/questions/3892/… But if you define singularities as infinitely small points which they may or may not be, would the two infinitely small points meet or will they only spiral ever closer? That's an interesting mathematical question that makes me think of Zeno and his silly paradox. – userLTK Feb 18 '16 at 15:27

We are therefore dealing with a $\frac{\mathrm{infinity}}{\mathrm{infinity}}$ problem, where a finite limit may, and in this case does exist.
Do not forget your $\lim$'s!