Transitivity (mathematics)


Transitivity (mathematics)

In mathematics, the word "transitive" admits at least three distinct meanings:

* A group "G" acts transitively on a set "S" if for any "x", "y" ∈ "S", there is some "g" ∈ "G" such that "gx" = "y". See group action. A somewhat related meaning is explained at ergodic theory.

* A binary relation is transitive if whenever A is related to B and B is related to C, then A is related to C, for all A, B, and C in the domain of the relation. See transitive relation.
* A transitive set is a set A such that whenever "x" ∈ "A", and "y" ∈ "x", then "y" ∈ "A". The smallest transitive set containing a set A is called the transitive closure of A.

ee also

* intransitivity


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