0.999...ad infinitum does NOT Equal 1!
You are wrong, 0.9 period equals 1.
Maybe think of it as 1=3*(1/3)=3*0,33333333..... =0,999999999.........
It is not even infinitesimally close, just theoretically approximate to 1. But is never ending and not truly equalling.
Here is the proof.
Let n be any whole number, then
((10)^n)-1))/(10^n)
Never converts to 1, or any other power of 10 !
Example:
9/10, 99/100...((10^n)-1)/(10^n)