Mathematics

A recurring conclusion in combinatorics education is the importance for students to attend to the set of outcomes that a counting problem counts. One way to do so is to list the outcomes, and then ask students to find which outcome is in the mth place (where m is a reasonably large integer). For counting problems solved by applying the multiplication principle, I will show that one solution method for these types of problems is to create positional representation systems for integers. By doing so, I will demonstrate how positional representation systems of integers correspond to enumerating sets of outcome. I will then demonstrate how the positional representational systems can be created to represent all real numbers.