- 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". Seegroup action . A somewhat related meaning is explained atergodic 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. Seetransitive relation .

* Ais a set A such that whenever "x" ∈ "A", and "y" ∈ "x", then "y" ∈ "A". The smallest transitive set containing a set A is called thetransitive set transitive closure of A.**ee also***

intransitivity

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