[Suppafly]

>So, in this view, 0.3 or 0.333... are not numbers in the proper sense, they're just a convenient notation for 3/10 and 1/3 respectively. And there simply is no number whose notation would be 0.999..., it's just an abuse of the decimal notation.

I wonder if students from Romania are hamstrung in more advanced mathematics from being taught this way.

[leereeves]

I don't think they would be; I think they might even have an advantage. They'd understand that the only numbers that have infinite repeating expansions are rationals, and that decimals are, in general, just approximations.

[tsimionescu]

I don't think decimals, especially repeated decimals or other infinite decimal expansions, show up much if at all in any advanced math subjects beyond the study of themselves, of course). Higher math is almost exclusively symbolic. You're more likely to need to learn that "1" is just a notation for the set which contains the empty set then to learn that it's OK to add 0.22... + 0.44... = 0.66...