No.
I disagree.
The point of contention is the standard meaning of the symbol that is (0.\dot9).
Obviously, I have to repeat it at least one more time: I am NOT talking about what I mean by (0.\dot9), I am talking about what mathematical establisment means by (0.\dot9).
That said, you might want to argue that I am wrong in my belief that mathematicians define (0.\dot9) as a sum and not as a limit.
The limit of a sum is not the sum itself.
You can call the limit of a sum by the name “sum” – and people already do that, I understand – but that doesn’t erase the difference between the concept of a sum and the concept of a limit.
Let me give you an analogy. You can call numbers horses. There’s nothing wrong with that. But you can’t say there’s no difference between numbers and horses.
The argument I’m putting forward is that (0.\dot9) represents THE RESULT OF A SUM and not THE LIMIT OF A SUM. They are two related but different things.
That said, you might want to argue that mathematicians interpret (0.\dot9) as the limit of a sum (and not as the sum itself.) By doing so, however, you would be making an exception for (0.\dot9) and similar expressions because all other decimal numbers are normally interpreted as sums.
The result of a sum is a number that is attained. The limit of a sum is a number that is approached – not necessarily attained.
Your best bet is to argue that (0.\dot9) represents a limit rather than a sum. You won’t get far by trying to deny the fact that the concept of limit and the concept of sum are two different concepts.