In mathematics, a binary relation R over a set X is euclidean if it holds for all a, b, and c in X, that if a is related to b and a is related to c, then b is related to c. This is different from the transitive property. However, if a relation is reflexive and symmetric, then it is euclidean if and only if it is transitive. To write this in predicate logic:
- <math>\forall a, b, c \in X,\ a \,R\, b \and a \,R\, c \; \Rightarrow b \,R\, c</math>
If a relation is euclidean and reflexive, it is also symmetric and transitive, hence an equivalence relation. "Sibling of" is a euclidean relation.
