That’s because there is no connection!
Mathematics, especially modern math, is highly abstract and not bound by any physical considerations. Nobody is saying – well at least I’m not saying – that .999… refers to anything in the real world. On the contrary, I maintain that it does not. Nor does 1! The fact that .999… = 1 is a formal exercise in pure math; and has no point of contact with the real world as described by contemporary physics.
Physics (\neq) Math.
Now of course you will say, well isn’t math used in physics and biology and economics and everyday life at the grocery store and so forth.
Yes. And this is a philosophical mystery. Why is it that math, which is ethereal, way out there, and free of any “ontological burden” to be about the real world; nevertheless turns out to be supremely useful, in fact essential.
This question is discussed in the famous paper of Eugene Wigner titled, The Unreasonable Effectiveness of Mathematics in the Natural Sciences.
The title says it all. Math is so abstract that it is unreasonable to think it applies the world; but it does.
So the best thing to do is remember that math has nothing to do with anything except itself. If others find it useful. the mathematicians are happy but that’s not their reason for doing math. Of course I’m exaggerating a position but I hope I’m making my point.
It’s the job of philosophy to explain why math, a purely conceptual enterprise, is useful at all. Much has been written.
Historically, people used to believe that math described the real world, and that math = physics.
The split between math and physics was caused by the advent of non-Euclidean geometry in the 1840’s. That’s when everyone realized that math could not provide certainty about the world; and that if math couldn’t, then NOTHING could.
That was the birth of postmodernism and the cultural relativism of contemporary society. If rationality can’t tell us what’s true, then maybe rationality’s just a tool of oppression and not a path to truth at all. This all started with non-Euclidean geometry.