From: Westbrick | #021
Well-said. So I take if you'd say it follows from this that if the term in question doesn't fall into the realm of real numbers, then this type of proof can't necessarily be applied?
0.999~ is real. It has no imaginary component.
If you want something more rigorous (which I've been deliberately trying to avoid), check out things like this:
http://en.wikipedia.org/wiki/Real_number#Completeness
You can apply that directly to show that 0.999~ is real.
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No amount of planning will ever replace dumb luck.