Euclidean relation

Euclidean relation

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.

See also

* Equivalence relation
* Transitive relation


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