The real issue is that we don't define the real number system before we use it. The fact that 0.999... = 1 is a consequence of a formal definition of decimal nu

The real issue is that we don't define the real number system before we use it. The fact that 0.999... = 1 is a consequence of a formal definition of decimal numbers. We can create a new definition of decimal numbers that does not satisfy this equation and use it in place of our current one. Let's imagine a new decimal number system with some vague notion of infinitesimal numbers. We lose some properties we enjoy in our current system but all of those properties still hold for numbers with no infinitesimal part. We can still use our every day numbers like nothing has changed yet we also have a notion to describe infinitesimal values. We can make statements like 1/3 is infinitesimally less than 0.333... and carry on like nothing else has changed. Now let's sit someone down, start with the rational numbers, introduce Dedekind cuts to define the real numbers and prove that in the real number system that 0.999... is exactly equal to one. Let's also convince them that the real numbers are the unique complete ordered field and that each of these properties are indispensable. Then they will believe that 0.999... should be equal to 1.