Euclidean relation
From Wikipedia, the free encyclopedia
This article does not cite any references or sources. (June 2007) Please help improve this article by adding citations to reliable sources. Unverifiable material may be challenged and removed. |
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:
If a relation is euclidean and reflexive, it is also symmetric and transitive, hence an equivalence relation.
"Sibling of" is a euclidean relation.