Re: the 0.999... snafu:
Asking whether or not 0.999... = 1 is the same as asking whether 1/∞ = 0.
1 - 0.999... = 0.000...1
No. Please go learn some more math so you know what you are talking about.
Also, 1/∞ = 0. Not infinitesimal, not undefined, it's 0
"Learn math or gtfo." brilliant constructive answer. Kari, I think you misunderstand that what I posted is entirely hypothetical. What people are implying when they say 1 is not equal to 0.999... is that there is an infinitessimal difference between it and 1. I just took the problem and rephrased it to better state the problem at hand. Why am I getting so much "derp, you can't do that," crap?
Also, I am a bit confused, are you saying the infinitesimal doesn't exist? If an infinitely large number exists, why doesn't an infinitely small number exist, and why can't they be multiplied to be 1?
That wasn't what I was saying, I was trying to say that what you wrote is entirely incorrect. You're confusing the set of real numbers with some extension of it that includes infinitesimal numbers. But that was never the point. The point is that in the set of real numbers, 0.99.. = 1.
Also in the set of real numbers, 1/∞ = 0. Infinitesimal numbers "exist", but not in the set real numbers. ∞ is also not an element of the set of real numbers, that's why, when working with it, certain operations have been exactly defined. 1/∞ = 0 because lim(x->∞)(1/x) = 0.
Also, writing the infinitesimal difference between 1/∞ and 0 in that extended set of the reals as 0.00...1 makes no sense as well. There is no 1 at the end, since there is no end. There's no way to write an infinitesimal number like you would write another real number. Just like you can't write infinity, which is why the symbol ∞ was introduced. What you mean when you say that 1/∞ is infinitesimal is that 1/∞ is as close as you can get to 0, without writing 0. It has no meaning however.