Category:Definitions/Connected Relations

This category contains definitions related to Connected Relations.
Related results can be found in Category:Connected Relations.

Let $\RR \subseteq S \times S$ be a relation on a set $S$.

Then $\RR$ is connected if and only if:

$\forall a, b \in S: a \ne b \implies \tuple {a, b} \in \RR \lor \tuple {b, a} \in \RR$

That is, if and only if every pair of distinct elements is comparable.