Today, I learned an important math lesson. Sometimes, you will have a really great mathematical demonstration or proof in mind. You will go to a lot of trouble to write it out in detail, showing how every step works. And then when you get to the last step, you will suddenly realize that it doesn't work after all, and you have to throw everything out.

There was going to be a real post today. Just as I was finishing it up, I realized it doesn't actually work. Since I don't have another post lined up, this is all I can post instead.

This has happened before. This will happen again. This is the way of math. All you can do is hope things go better next time.