(definition)
Definition: A binary relation R for which a R b and b R a implies a = b.
See also symmetric, irreflexive, partial order.
Note: The relation "less than or equal to" is antisymmetric: if a ≤ b and b ≤ a, then a=b. The relation "is married to" is symmetric, but not antisymmetric: if Paul is married to Marlena, then Marlena is married to Paul (symmetric), but Paul and Marlena are not the same person.
Equals (=) is antisymmetric because a = b and b = a implies a = b. Less than (<) is also antisymmetric because a < b and b < a is always false, and false implies anything.
Author: PEB
If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.
Entry modified Fri Dec 17 11:47:38 2004.
HTML page formatted Wed Oct 26 09:47:11 2005.
Cite this as:
Paul E. Black, "antisymmetric", from
Dictionary of Algorithms and Data
Structures, Paul E. Black, ed.,
NIST.
http://www.nist.gov/dads/HTML/antisymmetric.html
