= Transitive closure (relation)
{title2=$R^+=\bigcup_{n\geq1}R^n$}
{wiki=Transitive_closure}
= Transitive closure of a relation
{synonym}
The transitive closure of a relation connects $x$ to $y$ when a finite nonempty chain of $R$-steps leads from $x$ to $y$. Concatenation proves <transitivity>, and induction along a chain shows that any <transitive relation> containing $R$ contains $R^+$. This concerns closure of a relation, rather than the <transitive closure> of a set under membership.
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