I don't know what the conclusive argument is in the comment section, but as long as we're working in the field of real numbers, 0.999... would always be approximately 1. Not exactly 1.
If we move to the field of Natural Numbers, we find that speaking of 0.999... is absurd, but speaking of 1 is not.
So yes, limit, supremum, approximation, correct.
Equality, nah.
I don't know what the conclusive argument is in the comment section, but as long as we're working in the field of real numbers, 0.999... would always be approximately 1. Not exactly 1.
If we move to the field of Natural Numbers, we find that speaking of 0.999... is absurd, but speaking of 1 is not.
So yes, limit, supremum, approximation, correct.
Equality, nah.