Your way of thinking makes sense but you're interpreting it wrong.

If you can round up and say "0,9_ = 1" , then why can't you round down and repeat until "0 = 1"? The thing is, there's no rounding up, the 0,0...1 that you're adding is infinitely small (inexistent).

It looks a lot less unintuitive if you use fractions:

1/3 = 0.3_

0.3_ * 3 = 0.9_

0.9_ = 3/3 = 1