Euclidean relation

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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:

\forall a, b, c \in X,\ a \,R\, b \and a \,R\, c \; \Rightarrow b \,R\, c

If a relation is euclidean and reflexive, it is also symmetric and transitive, hence an equivalence relation.

"Sibling of" is a euclidean relation.

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