stoutfellow

Today, in calculus, I began discussing sequences and series. As a teaser, I described an argument that most of my students had probably seen and accepted in high school, and then handed them another argument, superficially parallel, which leads to an obviously false conclusion. I asked, "Why does this argument (pointing to the first one) work, while this one (pointing to the other) doesn't? I'll let you think about that." Then I dismissed the class. One of my students - the same one who caught on to what I was doing on the test a couple of weeks ago - grimaced at this.

Leaving the building, I saw him ahead of me. (The doors are glass; he was already outside.) He glanced back, saw me, and grinned. As I came through the door, he hurried back, pointed at me, and said, "It's the 'infinity minus infinity' case, right?" I said yes, although there was a bit more to it than that. He said, "Great! Now it won't be bugging me all night." He went on his way. As I headed back to my office, I was grinning as broadly as he had been.

Sometimes it's worth it.