2/3 I understand reflexive, transitive, and symmetric relationships.
But what is anitsymmetry?
\_ So symmetry is where aRb implies bRa (where a and b are in
some set, and R is a relation). Then antisymmetry is just that
if aRb then it is NOT the case that bRa... in other words,
aRb and bRa impies a=b. Check Mathworld. - rory
http://mathworld.wolfram.com/PartialOrder.html
\_ So does that mean antisymmetry implies reflexivity?
\_ No.
\_ For example, < is anti-symmetric but not reflexive.
\_ I always thought antisymmetry means not symmetry!!!
\_ Think about the difference between apathy and antipathy.
\_ a high school way to think about it is sin[x] in [x, -Pi, Pi]
is anti-symmetric, and cos[x] in [x, -Pi, Pi] is symmetric.
\_ An alternative is to think about it the right way.
\_ antisymmetry is when you buy a house, ring, etc etc and then
you get a divorce, pay alimony, lose a house, so on and so
forth. -bmg |