The Two Couriers Problem

A Problem of Division by Zero in Transmathematics

Abstract

The problem of the two couriers is an old introductory problem from basic algebra first described by Augustus de Morgan in 1828 in his algebra textbook. The two couriers problem is interesting in that three of the possible answers are interrelated:  zero, infinity, and undefined or indeterminate result. These three results relate to division from fractions; and more specifically, infinity and undefined or indeterminate result from division by zero.

The aspect of division by zero makes the two couriers problem an ideal one for independent, objective examination within the mathematical framework of transmathematics—where division by zero is defined and has specific mathematical properties. The application to the original problem of the two couriers using transmathematics provides further insight into the answers of infinity, and undefined or indeterminate result, and a contradistinction between the answers provided in conventional mathematics versus transmathematics.