(note: this post has been closed to comments; comments about it on other pages will be deleted!)
I really didn't think this would go this far. I've gotten thousands of hits in the last couple of days, with links to the original post showing up all over the place on link farms. I will post a longer response in a couple of day, but I don't have time right now because I'm on vacation.
I will, of course, continue to believe my original claim, and thanks to the math people who post to help me explain it. I will not be able to answer every single comment (I can't even keep up with reading them). I hope that some of the people who read the post, though, were enlightened at least a little bit by the formal view of this question (I know I didn't include all the formalities, but I wasn't writing for people that would want them; the formalities are there, but I'm not going to try to explain them. This wikipedia article does a good job, if you're interested).
Back in a few days....