Relation/Examples/Between

Example of Relation

Let $A$, $B$ and $C$ be sets of points on a plane.

Let $\RR \subseteq A \times B \times C$ denote the subset of $A \times B \times C$ defined as:

$\forall a \in A, b \in B, c \in C: \tuple {a, b, c \in \R}$ if and only if $a$ lies between $b$ and $c$

Then $\RR$ is an example of a ternary relation on $A \times B \times C$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): relation: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): relation: 1.