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Re: [math-learn] Transitive property of equality (was: Manipulatives)
Posted:
Nov 18, 2003 8:12 PM
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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, 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
http://clem.mscd.edu/~talmanl
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