Let’s be honest…there are certain subjects that a math-ish kind of blog must mention at some point. One of these obligatory topics happens to be the “0.9999999… = 1” proof. It’s one of those facts that delights the mathematically inclined. It’s sort of like the joke that Grandpa always tells when the family gets together: you know it’s coming, and you know how much pleasure he gets out of relaying the joke, but for goodness sake, this is the 99th time you’ve heard the punchline. At any rate, there is a set of about 15 math facts that people love to talk about simply because they’re all totaling mind-blowing or sound totally nonsensical. I tend to think that the “0.9999999… = 1” proof belongs in the latter category.
The previous digression leads me to mention the Things of Interest blog, and their absolutely fantastic post on various forms of the “0.9999999… = 1” proof. You can find that post here. In case one proof doesn’t do it for you, this site offers several, each of which occurs at a various level of mathematical rigor. There will definitely be a proof for you here that you’ll understand.