The right way to approach this is to ask a question: What does 0.999... mean? What is the mathematical definition of this notation? It's not "what you get when you continue to infinity" (which is not clear). It's the value your are approaching as you continue to add digits.
When applying the correct definition for the notation (the limit of a sequence) there's no question of "do we ever get there?". The question is instead "can we get as close to the target as we want if we go far enough?". If the answer is yes, the notation can be used as another way to represent the target.
When applying the correct definition for the notation (the limit of a sequence) there's no question of "do we ever get there?". The question is instead "can we get as close to the target as we want if we go far enough?". If the answer is yes, the notation can be used as another way to represent the target.