NIST

antisymmetric

(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


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Entry modified 17 December 2004.
HTML page formatted Fri Feb 23 10:06:07 2018.

Cite this as:
Paul E. Black, "antisymmetric", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/antisymmetric.html