Definition:Null Relation

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The null relation is a relation $\mathcal R$ in $S$ to $T$ such that $\mathcal R$ is the empty set:

$\mathcal R \subseteq S \times T: \mathcal R = \O$

That is, no element of $S$ relates to any element in $T$:

$\mathcal R: S \times T: \forall \tuple {s, t} \in S \times T: \neg s \mathrel {\mathcal R} t$

Also known as

This is also sometimes referred to as a trivial relation by some authors, but to save confusion it is better to use that term specifically to mean this one.

Other sources prefer to call it the empty relation.

Also see

  • Results about the null relation can be found here.