One problem repeatedy appearing in this thread is that the intuitive meaning of some of our words is not the same as the mathematical one. In particular (not that I would ever try to get us into a political discussion) it all comes down to precisely what the meaning of "is" is. Or "equals," more specifically.

In mathematics, "equality" means that no matter how small a difference you specify, the difference between the two objects under consideration is less than that. For the matter at hand, it translates as: no matter how close you want to require, the series 0.999999... is closer still to 1.000000... . And there is no "exactly 1"; it's just a convenient shorthand for the endless decimal 1.000000..., which is the same as 0.999999..., just written in a different way.

Mathematics has some very precise meanings for its words, if for no other reason than to resolve this kind of quandary. True, if you reject the mathematical definition of the word, the discrepancy won't go away. There is an underlying assumption of "under the rules of mathematics..." that some are invoking and others are ignoring.

"Infinite" and "infinity" are two other words that cause confusion, because the mathematical and the common meanings aren't quite the same.

See - it all comes back to words, after all!