4 ms·

I took discrete math last semester and part of the course focused on binary relations and their properties (reflexive, symmetric, transitive...etc). I saw stude

by bryik 9y ago

I took discrete math last semester and part of the course focused on binary relations and their properties (reflexive, symmetric, transitive...etc). I saw students memorize the mathematical definitions for all properties and yet be unable to actually apply them to a particular relation. I suspect many people ended up ignoring the definitions and coped by developing their own or using intuition. This seems like a sign that math is not being communicated effectively. "Translating" the math into Python code[1] helped me understand what these definition were saying and identify algorithms for exam time. The downside is that it took a lot of time and may not have been as effective as grinding practice questions. 1 - https://nbviewer.jupyter.org/github/bryik/jupyter-notebooks/blob/master/math/All%20Relations%20on%20a%20Set%20%28and%20Their%20Properties%29.ipynb https://nbviewer.jupyter.org/github/bryik/jupyter-notebooks/...

aaachilless 9y ago
IMO this is sort of an ironic example because it's a case where the names actually convey meaning well. It's a case where I've specifically noted to myself "I'll always remember these definitions because the names are so nice".
- bryik 9y ago
  What about symmetric vs antisymmetric? My professor even warned us about how the names can be misleading (it is possible to have a relation that is both symmetric and antisymmetric).
  - aaachilless 9y ago
    In this case there's not really a naming problem either. The confusion comes from the idea that ((A -> B) && (A -> ~B)) is sometimes true. Capturing that subtlety in a name doesn't seem practical to me.
    - 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 ago
        I 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.

by bryik 9y ago

aaachilless 9y ago

IMO this is sort of an ironic example because it's a case where the names actually convey meaning well. It's a case where I've specifically noted to myself "I'll always remember these definitions because the names are so nice".

bryik 9y ago
What about symmetric vs antisymmetric? My professor even warned us about how the names can be misleading (it is possible to have a relation that is both symmetric and antisymmetric).
- aaachilless 9y ago
  In this case there's not really a naming problem either. The confusion comes from the idea that ((A -> B) && (A -> ~B)) is sometimes true. Capturing that subtlety in a name doesn't seem practical to me.
  - 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 ago
      I 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.