Definition:Trivial Relation
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Definition
The trivial relation is the relation $\mathcal R \subseteq S \times T$ in $S$ to $T$ such that every element of $S$ relates to every element in $T$:
- $\mathcal R: S \times T: \forall \left({s, t}\right) \in S \times T: \left({s, t}\right) \in \mathcal R$
That is:
- $\mathcal R = S \times T$
... the relation which equals the product of the sets on which it is defined.
Sources
- Paul R. Halmos: Naive Set Theory (1960)... (previous)... (next): $\S 7$: Relations
