A danger in teaching familiar material is oversimplification. In this article, we shall explore an example of this. One of the authors observed a colleague (at another institution) introduce his students to the ordering of the real numbers by stating that < is a relation on ℝ which satisfies the following axiom system: “For all x, y, z in ℝ: 1. Exactly one of x = y , x < y , y < x holds. 2. If x < y and 0 < z , then xz < yz . 3. If x < y , then x + z < y + z .”