Yes, but at the same time it is common for people to insist that 0.999… only "approaches" unity as if it were a series approaching a limit, rather than an unique number. Intuition is a funny thing.
Saying "a number isn't a limit" is true, but it's only really relevant if you're talking to someone who genuinely has no idea what limits are. In actual math the number 0.99... can be defined as the limit of a series.
Every number is a limit, yes, but people think of 0.999… as a series. Not rigorously, of course, but that's a common argument even by people (perhaps especially by people) who have a highschool or even math-minor level understanding of series and limits.
