ABSTRACT
A primary goal of a first course in real analysis is to develop the theory of calculus with a rigorous mathematical approach. The “rigorous mathematical” approach is key here: oftentimes in a standard first-year calculus course, students learn rules and techniques without developing why these rules work. This chapter highlights the well-ordering principle of N; every nonempty subset of N has a least element. It also highlights the axiom of completeness. Every nonempty subset of R, an ordered field, that is bounded above has a least upper bound in R. Equivalently: Every nonempty subset of R that is bounded below has a greatest lower bound in R. The chapter also outlines the principle of strong mathematical induction.
