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I'm not sure I understand. The problem with symmetric/antisymmetric is that the names make students think they are related and this can lead to misunderstanding
by bryik 9y ago
I'm not sure I understand. The problem with symmetric/antisymmetric is that the names make students think they are related and this can lead to misunderstanding (e.g. "since this relation is antisymmetric, it cannot be symmetric"). Arguably, this confusion would not exist if they were named differently.
- aaachilless 9y agoI think maybe there's some confusion here regarding the definitions of symmetry and antisymmetry, because they're very closely related. Symmetry says "whenever A, then B" and antisymmetry says "whenever A, then not B". I.e, given a piece of information A, symmetry and antisymmetry tell you to draw opposite conclusions, which is why one is "anti" the other. The only time a relation can be both symmetric and antisymmetric is when the antecedent in their definitions is never true, which is the trivial case.