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xkcd #3283: Size and Lifespan
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Don't you mean the event horizon of the black hole? The actual matter of a black hole is in an infinitely small point, right?
The horizon is what defines the black hole. From the outside the mass distribution is not defined, as there isn't any experiment you can do that tells you about the internal structure. If you let a mass fall into a black hole you won't see it cross the horizon, just get asymptotically closer to it.
Very very small but not infinitely so. That would violate the Heisenberg uncertainty principle of quantum mechanics.