Regarding the ancient column (all the way back in '03) on .999 being equal to 1, “An infinite question: Why doesn’t .999~ = 1?”, in which the answer was that it IS equal to one, I gotta say, I’m spotting some faulty logic. It was obviously written by an impostor, not Cecil. The whole thing was arrived at by saying .333~ is equal to 1/3. Assuming that, you’re right, because as stated in the article:

.333~ = 1/3

.333~ + .333~ = .666~, or 2/3

.333~ + .333~ + .333~ (or .333~ + .666~, if you prefer) = 3/3

3/3 = 1

Now, before we go any further, I’d like to throw in the fact that more than one digit in these numbers is superfluous, because, as also stated in “Cecil’s” article, ~ means the decimal keeps repeating infinitely. But I split hairs here.

Now, why this cretin impersonating our (well, your) lord and master is wrong. It was ENTIRELY based on .333 being equal to 1/3. Well, I gotta tell ya, it’s not. 1/3 (obviously) means the number indicated is exactly one third of a whole number.

I know what you’re thinking now. “Oh mighty General, you have truly mastered the laws of mathematics. Your wisdom is far beyond the understanding of mortal man.” And you’re right. But please, keep the praise back until I’ve arrived at my point. My point is simply this: .333~, while damn close, is NOT 1/3 of 1. I mean, sure, it’s the closest thing we’ve got, and it works for all practical points and purposes (unless you’re way too much of a perfectionist for me to want you in my immediate area, but this article is all ABOUT perfection). .999~, while infinitesimally close to 1, will NEVER actually reach 1. Truth is, there’s no way for 1 to be divided into 3 EXACTLY equal portions. It’s just that, as I said before, .333~ is the absolute closest thing we have, and, as I also stated before, it works in every situation except this one, where we’re just splitting hairs for the fun of it, so .333~ is generally accepted as 1/3.

So in short, your calculations were entirely correct, but they were based on a widely accepted inaccuracy. Go forth and use this newfound knowledge. Probably on one of your mathematician friends who’s getting too big for his britches.