Category:Definitions/Euclidean Relations

This category contains definitions related to Euclidean Relations.
Related results can be found in Category:Euclidean Relations.

Let $\RR \subseteq S \times S$ be a relation in $S$.

$\RR$ is left-Euclidean if and only if:

$\tuple {x, z} \in \RR \land \tuple {y, z} \in \RR \implies \tuple {x, y} \in \RR$

$\RR$ is right-Euclidean if and only if:

$\tuple {x, y} \in \RR \land \tuple {x, z} \in \RR \implies \tuple {y, z} \in \RR$

$\RR$ is Euclidean if and only if it is both left-Euclidean and right-Euclidean.