Definition:Relational Structure
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Definition
A relational structure $\left ({S, \mathcal R}\right)$ is a set $S$ together with a relation $\mathcal R$ on $S$.
Technically, $\left ({S, \mathcal R}\right)$ is an ordered pair:
- The first element of the pair is the set $S$.
- The second element is the relation $\mathcal R$, which is itself a set of ordered pairs (being a subset of the cartesian space $S^2$).
Sources
- Seth Warner: Modern Algebra (1965)... (previous)... (next): Exercise $14.9$
