[atq2119]

An alternative to the sibling comments:

In this context, the notation 0.999... does not represent a process. It represents a fixed number.

Which number? Well, if you reason through it you'll find that it has to be the same number as that represented by the notation 1.

An insight that is crucial (and pretty obvious in hindsight, though many people seem not to be exposed to it) is to distinguish between a number and its representations. "1" is not a number, it is merely the representation of a number. And numbers have many different representations. As a member of this forum, you can probably appreciate that "12" and "0xC" are two different representations of the same number. In the same way, 0.999... and 1 are different representations of the same number.