Definition:Total Relation

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Definition

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


Then $\RR$ is defined as total if and only if:

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


That is, if and only if every pair of elements is related (either or both ways round).


Also known as

Other terms that can be found that mean the same thing as total relation are:

Some sources use the term dichotomy, but this word is also used for a concept in statistcis, so will not be used in this context on $\mathsf{Pr} \infty \mathsf{fWiki}$.


Also see

  • Results about total relations can be found here.


Sources