Definition:Agreement

Definition
Let:


 * $$\mathcal R_1 \subseteq S_1 \times T_1$$ be a relation on $$S_1 \times T_1$$;
 * $$\mathcal R_2 \subseteq S_2 \times T_2$$ be a relation on $$S_2 \times T_2$$;
 * $$X = S_1 \cap S_2$$.

If:


 * $$\forall s \in X: \mathcal R_1 \left ({s}\right) = \mathcal R_2 \left ({s}\right)$$

then the relations $$\mathcal R_1$$ and $$\mathcal R_2$$ are said to agree on or be in agreement on $$X$$.

Note
The concept is usually seen in the context of mappings.