A Quirky Function

guest post by David Tanzer

Here is a mathematical riddle. Consider the function below, which is undefined for negative values, sends zero to one, and sends positive values to zero. Can you come up with a nice compact formula for this function, which uses only the basic arithmetic operations, such as addition, division and exponentiation? You can’t use any special functions, including things like sign and step functions, which are by definition discontinuous.

In college, I ran around showing...