Epsilon

Years ago, when I taught calculus, I’d usually include the following extra credit question on the first exam: “In the small box, write a good value for . A valid answer gets 4 points; the smallest answer in the class will get 5 points.” It was basically free extra credit… any positive number would work, but it was a (hopefully) fun way for students to be a little competitive in coming up with small positive numbers, which is the intuitive meaning of in mathematics. (I still remember when my high school math teacher was giving me directions to a restaurant, concluding “You’ll know you’re within of the restaurant when you see the signs for Such-and-Such Mall.”)

Most students volunteered something like or . Except for one particularly gutsy student who wrote, “The probability that Dr. Q gets a date on Friday night.” For sheer nerve, he got the 5 points that year.

Also getting 5 points that year was the best answer of the class: “Let be the smallest answer that anyone else wrote. Then .” That was especially clever from a calculus student, as that’s the essence of a fairly common technique when writing proofs in real analysis.