"0.9999999... is not equal to 1"

Rob, yes it is. The argument is very simple.

x = .99999...

10x = 9.9999...

10x - x = 9.9999... - x
(but x is just .9999...)

9x = 9

x = 1

Therefore x = 1 and x = .99999...

The only way this could happen is if 1) I've made a mistake in the math, or 2) the numbers are indeed the same.

If I've made a mistake in the math, please point out the specific property or postulate that I'm violating.