Notice that you write 0.9... with dots instead of just writing the number... because it isn't a "normal" number. Of course I agree, it approaches 1 for any numb

Notice that you write 0.9... with dots instead of just writing the number... because it isn't a "normal" number. Of course I agree, it approaches 1 for any number of digits. But infinitely many digits are not a number of digits. Please, define the exact meaning of the ... you use.