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*Proposition:*
Let `R` be a binary relation on `S` where `S` has `n`
elements. Then **union**_1 <= `i` <= `n` `R`^{i}_{S} is the
transitive closure of `R`:

forallS,R:RsubsetSxS=>transitive _{S}(R) =union_1 <=i<=nR^{i}_{S}wheren= |S|.

*Interpretation:* Transitive closure is limit of

[ R,Runion (RoR), ...,Runion (RoR) union ... unionR^{n}]

*Constructive method for computing transitive closure.*

Author: Wolfgang Schreiner

Last Modification: January 26, 2000