That's a good one - I mainly used the one-third proof because it was dead easy to transition to. Edit: Also, because it emphasized my point - which is that allowing recurring decimals at all implies one equals point nine recurring.

Another one for your viewing pleasure:

Let x = 0.999...
      =  0.9  +   0.09   +   0.009    + ...
      = 1-0.1 + 0.1-0.01 + 0.01-0.001 + ...
      = 1