Published online by Cambridge University Press: 03 November 2016
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.”