(definition)

**Definition:**
A *binary relation* R for which a R b and b R c implies a R c.

**See also**
*reflexive*, *symmetric*.

*Note:
The relation "less than" is transitive: if a < b and b < c, then a < c. The relation "is an ancestor of" is also transitive: if Reuben is an ancestor of Bill and Bill is an ancestor of Patrick, Reuben is an ancestor of Patrick. However "likes" is not transitive since someone I like may like someone that I don't like.*

Author: PEB

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Entry modified 17 December 2004.

HTML page formatted Fri Feb 23 10:06:08 2018.

Cite this as:

Paul E. Black, "transitive", 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/transitive.html