Transitive Closure Always Exists (Relation Theory)/Proof 1
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|This article has been proposed for deletion. In particular: |
There is no mathematical difference between this and Transitive Closure Always Exists (Relation Theory)/Proof 2 -- the latter is merely an expanded and more rigorous version of this.Please assess the validity of this proposal. (discuss)
Then the transitive closure $\RR^+$ of $\RR$ always exists.
First, note that there exists at least one transitive relation containing $\RR$.
Next, note that the Intersection of Transitive Relations is Transitive.