Berkeley CSUA MOTD:Entry 23770
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2025/07/09 [General] UID:1000 Activity:popular
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2002/2/4-5 [Recreation/Dating] UID:23770 Activity:very high
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
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mathworld.wolfram.com/PartialOrder.html
Foundations of Mathematics 10 Geometry 11 History and Terminology 12 Number Theory 13 Probability and Statistics 14 Recreational Mathematics 15 Topology 16 Alphabetical Index ABOUT THIS SITE 17 About MathWorld 18 About the Author 19 Terms of Use DESTINATIONS 20 What's New 21 MathWorld Headline News 22 Random Entry 23 Animations 24 Live 3D Graphics CONTACT 25 Email Comments 26 Contribute! For a partial order, the size of the longest 34 chain ( 35 antichain) is called the 36 partial order length ( 37 partial order width).