> Why do we accept .999... as a valid notation. Why not only allow 1 to denote this concept? That would be adding a special rule for purely cosmetic reasons.

> Why do we accept .999... as a valid notation. Why not only allow 1 to denote this concept? That would be adding a special rule for purely cosmetic reasons. It's typically not done in mathematics, where concise rules are usually more cherished than special-casing things.