Definition:Relation/Relation as Subset of Cartesian Product

Definition
Most treatments of set theory and relation theory define a relation on $S \times T$ to refer to just the truth set itself:
 * $\mathcal R \subseteq S \times T$

where:
 * $S \times T$ is the Cartesian product of $S$ and $T$.

Thus under this treatment, $\mathcal R$ is a set of ordered pairs, the first coordinate from $S$ and the second coordinate from $T$.

This approach leaves the precise nature of $S$ and $T$ undefined.

While this definition is usually perfectly adequate, on the full formal definition is preferred.

There may be many places on where this simplified approach is taken. However, there exists an ongoing maintenance task to address this.