1-(1*10^-∞) where (1*10^-∞) ≠0 , so 1-(1*10^-∞)≠1-0, so 1-(1*10^-∞)≠1 and finally 0.9~≠1
The fact on experimental measurement 0.9~=1 its just because it doesn't matter, they are NEARLY the same and theres infinitesimal difference between them. But mathematically they are not the same for obvious reasons.