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Proposition: Let R be a binary relation on S where S has n elements. Then union_1 <= i <= n RiS is the transitive closure of R:
forall S, R: R subset S x S => transitiveS(R) = union_1 <= i <= n RiS where n = |S|.
Interpretation: Transitive closure is limit of
[R, R union (R o R), ..., R union (R o R) union ... union Rn]
Constructive method for computing transitive closure.