Transitive closure

Smallest transitive relation containing a given binary relation

Summary

In mathematics, the transitive closure R+ of a homogeneous binary relation R on a set X is the smallest relation on X that contains R and is transitive. For finite sets, "smallest" can be taken in its usual sense, of having the fewest related pairs; for infinite sets R+ is the unique minimal transitive superset of R.

Originally created by 128.175.112.225

8/9/2003, 3:57:03 AM

Modified

1/15/2026, 9:57:24 PM

Contributors

Source: WikipediaView full article