Benoit, those are two different ways of writing the same real, just like 0.333... and 1/3 (or 1.0/3.0, if you insist) are the same number. That's not a paradox. 2 is a computable number, and thus so are 2.000... and 1.999..., even though you can't write down those ways of expressing them in a finite amount of time. See the definition of a computable number if you're confused.

1.999... = 2.000... = 2. Period.