Definition:Relation/Abuse of Notation
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Abuse of Notation for Relation
By abuse of notation, the usual technique for denoting a relation $\RR$ on $S \times T$ is:
- $\RR \subseteq S \times T$
thereby endorsing the approach of defining a relation as a subset of a Cartesian product.
Similarly, it is equally common to denote the expression $s \mathrel \RR t$ as:
- $\tuple {s, t} \in \RR$
While this approach conflates the relation with its truth set, it is sufficiently convenient and widespread as to be endorsed by $\mathsf{Pr} \infty \mathsf{fWiki}$.
We have not been able to find more mathematically rigorous notations for this that are at the same time not overly unwieldy.