The Hyphenator wrote:
((Also, did you really see the 2nd iteration of your sig first? I've only seen people with 17 or higher.
Yup. Or at least, the first time I saw this sig it was from someone who *claimed* to have seen the 1st iteration. I had just happened to peek into News & Events one day (not a forum I regularly check), when I saw someone with Gen2. I can't remember who it was precisely, but it was a regular poster round these parts ("these parts" being Math, Science, Coding, or Comp Sci). My instinct is to say Gelsamel, but that can't be right unless he's recently changed his sig.
I didn't see all the Gen17's show up until about a week later, I think. It was several weeks after that that I finally broke down and added the line to my own sig. Unfortunately, it roughly corresponds to when I started seeing people knowingly perverting the system with Gen -3+i and stuff.
Note, though, that I browse at work with a custom stylesheet that hides signatures, so people may have been floating around with the things for a long time without me seeing them. It's only here at home (on Chrome, where user stylesheets aren't yet supported) that I see people's signatures (or avatars, or many other things. I'm very much a fan of minimalism, especially when it help to hide what I'm doing from casual onlookers.)
Edit: Crap, what I worked out above is incomplete. I left out the case of BAs x/y and (x+1)/y, with bound y. These produce an ambiguous number. Frex, 1/4 and 2/4 are BAs for the ambiguous number 3/8.
So, an ambiguous number is produced by the numerators differing by 1, the denominators differing by 1, or both. I've already established that having the numerators or denominator differing by more than 1 does *not* produce a pair of numbers which are BAs for some ambiguous number, and clearly having numerator and denominator both equal doesn't work either (as the "two" numbers are just 1, and are an exact approximation). That truly does cover every case, then.