> I'm going to be charitable and assume that you didn't get my > argument. 1 and 2 is to the right of all of the segments > ([1-1/10^(n-1), 1-1/10^n])n?N, 0.999... is not.
Is 0.999... =< 0.9 ? No, because 0.99 Is 0.999... =< 0.99 ? No, because 0.999 Is 0.999... =< 0.999 ? No, because 0.9999 ...
If 0.999... has a value, that value is not less than 1.
By a separate argument, if 0.999... has a value, that value is not larger than 1.
If you say that 0.999... has a value, that value is 1.
If you _don't_ say that 0.999... has a value, then you have not defined 0.999... , and you should stop saying that 0.999... means infinitely many commands, not even for _what you mean_ because there _is no_ "what you mean".
Anyway, whatever it is you mean or don't mean is beside the point, which is that _the standard meaning_ of 0.999... does not mean infinitely many commands.
This is actually a better reason to stop saying that, but it looked for a moment as though you intended your infinite sum 0.9 + 0.09 + 0.009 + ... to mean something. I just wanted to point out that, if it means something, it means 1.