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Transitive Closure

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.

Author: Wolfgang Schreiner
Last Modification: January 26, 2000

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