> The definition of equivalence relation, total ordering, and > so on, don't seem to be to be things that belong in an > algebra 1 course, or geometry or algebra 2 for that matter.
On the other hand, non-trivial equivalence relations, et al, very much belong in these courses. Similarity, for example, belongs in a geometry course. And I submit that there is no reason why we should not observe that a geometric figure is similar to itself; that whenever figure one is similar to figure two, then figure two is similar to figure one; and that whenever figure one is similar to figure two, which in turn is similar to figure three, then figure one is similar to figure three. I don't much care whether we call these properties "Reflexivity", "Symmetry" and "Transitivity", respectively, or not at this level. There is plenty of time for the official math-speak terms later on.
--Lou Talman Department of Mathematical and Computer Sciences Metropolitan State College of Denver