Neither of those examples use the rules of those system though.
Basic arithmetic on decimap notation is performed by adding/subtracting each digit in each place, or multiplying each digit by each digit then adding those sub totals together, or the yet more complicated long division.
Adding (and by extension multiplying) requires the carry operation, because digits only go up to 9. A string of 9s requires starting at the smallest digit. 0.999… has no smallest digit, thus the carry operation fails to roll it over to 1. It’s a bug that requires more comprehensive methods to understand.
Someone using only basic arithmetic on decimal notation will conclude that 0.999… is not 1. Another person using only geocentrism will conclude that some planets follow spiral orbits. Both conclusions are wrong, but the fault lies with the tools, not the people using them.
I mean those more advanced methods are taught after basic arithmetic. There are plenty of adults that operate primarily with 5th grade math, and a scary number of them do finances…
This isn’t about limits of accuracy, we’re working with abstract values and ideal systems. Any inaccuracies must be introduced by those systems.
If you think the system isn’t at fault here, please show me how basic arithmetic can make 0.999… into 1. Show me how the carry method deals with Infinity correctly. If every error is just using the system incorrectly, then a correct use of the system must be applicable to everything, right? You shouldn’t need a new system like algebra to be correct, right?