The use of the dyadic partition in elementary real analysis

In Gordon (1998), Gordon presented alternate proofs of several well known results in elementary real analysis using tagged partitions. In this paper, we provide a set of alternative proofs based on the dyadic partitions. An important difference between tagged and dyadic partitions is that the results based on the dyadic partition can be obtained constructively, i.e. an algorithm is supplied to reach the conclusion of each proof. In addition, the construction involves only concepts and results presented in a first course real analysis, which is the reason why, comparing tagged partition and its theory, the proofs based on dyadic partition are more straightforward and accessible to a wide range of audience.