(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