1.9999... = 2 is not an "issue" or a "paradox" in mathematics.

If you use a limited number of digits in your calculations, then your quantization errors can accumulate. (And suppose the quantity you are measuring is the difference of two much larger numbers.)

Of course it's possible that there's nothing in the real world that corresponds exactly to our so-called "real numbers". But until we actually know what smaller-scale structure it is that we're approximating, it would be crazy to pick some arbitrary "lower-resolution" system and hope it matches the world better. That's doing for "finiteness" what Eliezer has somewhere or other complained about people doing for "complexity".