1 = 0,99........

[Bridge]

So while it seems counter intuitive. It is mathematically solid.

Because you assume 0.00 … 01 is "infinitely small". I assure you, if you actually used the real number that is being represented, you would not get the solution "1=0.9~". It's like saying:

1/inf x + 1 = 1
0 + 1 = 1
1/inf x = 0

Nobody can say this isn't valid because the number is not calculable and therefore the solution unknowable. 1 divided an infinite amount of times is also an infinitesimal (perhaps even the same number), but it is most certainly not zero. This is an assumption that the solution needs in order to work. It's a loss of data, no matter how much you say it isn't because it "never reaches the last digit" (now there's an absurd mathematical concept for you).