In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

Today’s quip is a light-hearted one-liner that I’ll use to lighten the mood when in the middle of a complex calculation, like the following limit problem from calculus:

Let . Find so that whenever $|x-2| < \delta$.

The solution of this problem requires isolating in the above inequality:

At this point, the next step is dividing by . So, I’ll ask my class,

When we divide by , what happens to the crocodiles?

This usually gets the desired laugh out of the middle-school rule about how the insatiable “crocodiles” of an inequality always point to the larger quantity, leading to the next step:

,

so that

.

Formally completing the proof requires starting with and ending with .

I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.
View all posts by John Quintanilla

## 2 thoughts on “My Favorite One-Liners: Part 99”