0.9999……（无限循环）≠1?

0.9999……（无限循环）≠1?
1.因为 x = 0.9999...
2.所以 10x = 9.9999...
3.所以 10x - x = 9.9999...- 0.9999...
4.所以 9x = 9
5.所以 x = 1
我是个文盲,上过学的麻烦帮我解释一下1至5步,哪一步骤出现错误了么?
Proof:0.9999...= Sum 9/10^n
(n=1 -> Infinity)
= lim sum 9/10^n
(m -> Infinity) (n=1 -> m)
= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)
= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)
= .9/(9/10)
= 1
我找到了一个答案 似乎国外的科学家证明出0.9999……（无限循环）=1了