I'm writing a new Mathematical Enchantments essay titled "The One About .999..." and would love to get your feedback. I plan on publishing it in a week or so. Please leave your feedback here (and include your name in your comments so I'll know whom to acknowledge): https://mathenchant.wordpress.com/?p=142&shareadraft=55f327dde83a0 Or you can post comments to math-fun, or in private email to me, if you prefer. Thanks, Jim Propp P.S. I'm sure I've seen a slicker and easier-to-follow bogus analysis of 1 - 1/2 + 1/3 - 1/4 + ... than the one I give in the End Notes; my high school math teacher Mr. Brenner showed it to me forty years ago, but for some reason I'm unable to reconstruct it. I'm sure it's out there, in print if not on the web. Can anyone provide a lead?