Is 0.999999999…… equal to 1 ？

Of course not
but, I wonder how to explain following processes:


Set x=0.99999999999999……；
then 10x=9.99999999999……；
so that 10x - x = 9x = 9.99999999…… - 0.999999999…… = 9；
so x = 1；

Because 0.99999999999…… + 1 = 1.99999999999999……
because 0.99999999999…… + 0.99999999999…… = 1.999999999999……，too；
so that 0.99999999999…… = 1；

Why？
Who can tell me？