On the dovetail counting method

When the idea of dovetailing is introduced to the student, they can recognize that this method shows a way to count the set of positive rational numbers, but would typically have questions about the counting specifics. Unfortunately, information about such specifics is generally not available to the student and instructors. In this paper, we (1) identify the problems associated with the dovetail method, (2) solve the problems mathematically, (3) implement the mathematical solution using the programming language ML, and (4) summarize the contribution of the paper. This paper can be used as a tool or reference in introducing the dovetail method to the student and in dealing with the ensuing issues.