That doesn’t explain why you think it’s “technically countable”.
If you can count it, then you can identify it. Countable and identifiable seem to go together.
The text in red is inserted by me.
I agree that the conclusion follows from the premises and I agree with the second premise. What I disagree with is the first premise. That said, it is up to me now to present an argument against it. Wait for it 
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What is there is not necessarily seen.
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Therefore, if there was a (0) associated with (10^0) in (99\dot9), obsrvr524 would not necessarily see it.
Take THAT! 
I don’t think that you are using it in that sense. Basically by writing infA-1, you’re counting backwards from infA. That seems like a no no. You know, counting back from where exactly??
But I was hoping that you would skip that obvious argument.
If that is where you want to go and have nothing else to offer then you have expired your defense on that issue by not convincing me of your premise (4) - so the rest of that argument (version 4) is moot.
Do you have a different argument to make addressing the proposal? If so - it’s time to post it. 
I made that argument myself much earlier. I don’t use (infA-1) as an index for that reason - but Magnus does.
Your definition for 999… has infinity+1 digits.
Whatever that means. 
I tend to think that 999… is just infinity. (As is any number represented as n…)
I used the term “positive number” to mean “a number greater than or equal to (0)”. That does not have to be a natural number. For example, (1.5) is not a natural number but it is a positive number.
The conventional meaning of the term “positive number” is not relevant though I do think that it is the same as the one assigned by me.
Perhaps you already forgot what you wrote. Perfectly normal as we age, think nothing of it. Let me help you out.
Emphasis mine.
I reiterate: If you are making up your own kind of numbers, you are free to do so if you can make them logically coherent, which you have so far failed to do. But if you are talking about the standard natural numbers, as you clearly seem to be, each and every one of them has finite length.
I didn’t forget what I wrote.
Yes, I spoke of base-10 numerals that stand for positive numbers and that have no fractional part.
If a base-10 numeral has no fractional part, it does not mean it represents a natural number.
Can you explain the bolded part?
You agree that you are NOT talking about natural numbers, and you haven’t given a coherent definition of “9999999…”
But you know if you are really interested in making sense of numbers with infinitely many digits to the left of the decimal point, you might be interested in the p-adic numbers.
I am not interested in p-adic numbers. I am interested in you explaining what’s wrong with what I am saying (if you are interested, that is.) And note that “explaining what’s wrong with what I am saying” has a very specific meaning.
Yes, I am not talking about natural numbers. What about that?
As for (99\dot9), it’s a numeral that involves an infinite number of (9)s in the direction of the least significant digit. The weight of the first digit (and by extension, the weight of all other digits) is not specified and neither is the exact number of (9)s (we only know the number is greater than every integer.) That makes it a class of numbers rather than some specific number. What’s incoherent about that?
I couldn’t find your definition but I seem to recall it involves expressions like (10^\infty) which makes no sense. If you have a more current definition I did not take the trouble to read back to find it. If all you mean is that it’s infinite, then not much harm is done, but you seem to mean something more specific than that.
An implicit digit is a digit that is implied by the symbol rather than explicitly stated by it.
For example, in the case of (1), there is exactly one explicit digit – that digit is (1). But there are lots of implicit digits. For example, the digit immediately before it is (0). The digit associated with (10^{-1}) is (0) too. And so on.
Similarly, in the case of (999\dotso), there are three explicit digits (the three (9)s), many implicit (0)s and lots of (9)s implied by the ellipsis.
The problem with that is that the ellipsis in (999\dotso) indicates that the digits expand endlessly in the direction of the least significant digit. This means that they can’t stop at (10^0). The (9) associated with (10^0) CAN’T be the last (9) because there is NO last (9). That’s what the symbol is saying: no last (9).
Cool. But why do you think it makes no sense? It merely stands for (10 \times 10 \times 10 \times \cdots). It’s (10) multiplied by itself infinitely.
Because “10 multiplied by itself infinitely” is not defined anywhere.
Multiplication is defined as a binary operation. It inputs two numbers and outputs a third. 3 x 5 = 15. Two inputs, one output.
By induction we can extend the definition to any finite collection of input values. To show that 2 x 3 x 5 makes sense we note that it’s (2 x 3) x 5. And 2 x 3 is defined because it’s two inputs, so we get 6 x 5, which is again two inputs, so we get 30. We can use the associative law to note that we could have done it as 2 x (3 x 5) and the answer would be the same.
You have not defined “10 multiplied by itself infinitely.” All we can do with the standard rules of math is show by induction that any FINITE number of numbers multiplied together can ultimately be reduced to a sequence of binary operations.
So if you want to extend the definition to infinitely many multiplicands, you have to make a definition. And this you have not done. Which is why I say you haven’t done it.
You have an intuitive idea of what you mean, but you haven’t formalized it logically. And till you do that, you haven’t got a definition.
I agree that (\infty ) cannot be used as a number because it is not well defined.
(infA) is a different story.
I explained why that red clause is not true in the partial post you just quoted. If you have some rebuttal to that explanation - give it.
That might be true except that you specified “NO FRACTIONAL DIGITS” - that means there is no “9.###” but merely “9.” And your “…” actually bumped your “999” upward from 0 to make it an infinite count. If the “…” is allowed to go below zero then your number “999…” is undefined and can’t be rationally discussed. There is no way to know how big it is. It could just stand for “9999.9999…” or “999.999…” or any other amount. But in no case is there a 0 digit involved.
I disagree.
It can be used but it has its limits.