Im trying to make the distinction between a function that approaches a value as it's input grows, for instance a sequence seen as a function on the domain of the natural numbers, and the value itself.

I have seen a lot of people view 0.999... as a number that "approaches one", so formally speaking as the sequence (0.9, 0.99, 0.999, ...) and not the number itself which that sequence approaches which they would agree is 1.

The "its the largest number which is less than 1" type of thinking.