John Hodgman was interviewing Steven Strogatz about mathematics and his book The Joy Of X, and the discussion came around to the statement that the number one is actually equal to the number 0.99999... repeating infinitely. Steven Strogatz asked if anyone in the audience had a "favorite proof" of this and, well, I indeed have one.
So I got to stand up, find a microphone, and stumble quickly through the proof. I was amazingly nervous -- being on a mic in a room with a few thousand people explaining a math proof to a well-known mathematician will make you nervous, as it turns out -- and I feel like I wasn't very clear about the whole thing, but John Hodgman made some very funny "WHA?" noises and both men on stage seemed to understand what I was saying and roll with it. And people clapped. So all in all it was a win.
The proof goes like this:
I've always thought that was a neat equation, and quite frankly it's about all I remember from my infinite series and sequences class in college. Math is cool.