Grishka, I would have thought that my method was more accessible to other readers than the epsilon stuff. I reproduce it here -

1/9 = 0.1111....
9 * 1/9 = 9 * 0.1111....
1 = 0.9999....

I may have been a bit sloppy with the notation for recurring. It could have been -

1/9 = 0.(1)
9 * 1/9 = 9 * 0.(1)
1 = 0.(9)

but I think people knew what I meant.

I'm still unclear as to what is specfically dodgy about it.