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Re: [mathlearn] Transitive property of equality (was: Manipulatives)
Posted:
Nov 18, 2003 8:12 PM


From: Joshua Zucker <joshua.zucker@stanfordalumni.org>
> 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, nontrivial 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 mathspeak terms later on.
Lou Talman Department of Mathematical and Computer Sciences Metropolitan State College of Denver
http://clem.mscd.edu/~talmanl
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