Definition:Agreement

Definition

Relations

Let:

$(1): \quad \RR_1 \subseteq S_1 \times T_1$ be a relation on $S_1 \times T_1$

$(2): \quad \RR_2 \subseteq S_2 \times T_2$ be a relation on $S_2 \times T_2$

$(3): \quad X \subseteq S_1 \cap S_2$

Let:

$\forall s \in X: \map {\RR_1} s = \map {\RR_2} s$

where $\map {\RR_1} s$ denotes the image of $s$ under $\RR$:

$\map {\RR_1} s := \set {t \in T: s \mathrel {\RR_1} t}$

Then the relations $\RR_1$ and $\RR_2$ are said to agree on or be in agreement on $X$.

Mappings

The concept is usually seen in the context of mappings:

Let:

$(1): \quad f_1: S_1 \to T_1$ be a mapping from $S_1$ to $T_1$

$(2): \quad f_2: S_2 \to T_2$ be a mapping from $S_2$ to $T_2$

$(3): \quad X \subseteq S_1 \cap S_2$

Let:

$\forall s \in X: \map {f_1} s = \map {f_2} s$

Then the mappings $f_1$ and $f_2$ are said to agree on or be in agreement on $X$.