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Davman said:
The problem is that you don't understand you cannot replace 0,999.... with x during the solution.

Fine, if you don't believe that proof (and it is correct), then how about the second proof. What's wrong with that?

Davman said:
x is the number you are looking it is unknown.

x isn't unknown, because I've defined x to be 0.999...

"If x=0.999... then"