^ That's where you made your error, if you multiply X and the value of X in this equation by 10, that means there's 1 less '9' than in just X, infinity - 1 '9's, if that helps; so 10X-X (9X) would equal 0.000...1 in the infinity place, basically.RJ 17 said:Subtract x from both sides.
9x = 9 (10x - x = 9x, 9.999rep - x (which was originally stated as = 0.999rep) = 9)
You're dealing with infinitesimals here, and of course by definition infinitesimals can't be measured, and so will lead to errors if you try to use them in equations.
In short, .999... does NOT = 1, OP is wrong.