So, you're saying under SOME conditions 0.999... =1, and under other conditions, it does not =1.
I hate to point this out, but you are beginning to sound an awful lot like John Kerry ("Well, you see Larry, sometimes I support the war, and sometimes I don't....")
0.999.... has an infinite number of "9's" to the right of the decimal place UNDER ALL CONDITIONS and at ALL TIMES. It's exact value isn't wandering around. 0.999... =0.999... under ALL conditions. So how can it equal, and not equal, "1" depending on "circumstances"?
Simple. When you get to the end of the infinite series, you sneak in an extra digit when no one is looking.
Some people can't count up to one.
i do think i found why its so hard for your people to go with what i am saying. i am using a real world application, that is, science and philosophy. you are only working in science. this is my bad for not recognizing the blend when showing math.
I'm not going to bother with checking if i used the word "circumstance" or not. if i did, i shouldn't have. its not under a specific way of looking at it if they are equal, its more a matter of whats "good enough" for a specific application.
cutting an apple into thirds by hand is not exact, but it can be "good enough" to be fair. i am also not stating i support one thing over the other, i am showing that things aren't always what we claim. it is an unbiased observation, not an opinion.
Kerry swings his opinion like a hammer (a single war, which has not changed circumstance, he has gone back and forth supporting) i am steadfast that math is subjective depending on the application involved. (an idea of numbers is different, depending on the usage)
its like the joke about the man in the woods who has a philosopher, an engineer, and a physicist walk in and see his wood-burning stove is 3 feet above the ground.
the scientist looks at it and says "ah, this man knows heat radiates, so he wants to spread the heat as far as he can by raising it."
the philosopher says "no, he obviously wanted the heat and light to provide him with a new view of life, so he raised it to look at things in a new way."
and the engineer said "no, no, no, you both got it wrong, he raised it because it gets real cold here at night, he sleeps under it to keep warm at night"
the man speaks up at this point, and points out "actually, i just ran out of pipe."