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  1. ∈ R, if, x ≥ y defined on the set of +ve integers is a partial order relation.[1]
  2. : Show that the relation 'Divides' defined on N is a partial order relation.[1]
  3. Thus, the relation being reflexive, antisymmetric and transitive, the relation 'divides' is a partial order relation.[1]
  4. The set A together with a partial order relation R on the set A and is denoted by (A, R) is called a partial orders set or POSET.[1]
  5. A partial order on a set is a way of ordering its elements to say that some elements precede others, but allowing for the possibility that two elements may be incomparable without being the same.[2]
  6. The set of events in special relativity is described by a partial order.[3]
  7. Example 2 Determine whether the relation \(R\) represented by the matrix is a partial order.[3]
  8. Prove that \(R^{-1}\) is also a partial order.[3]
  9. Determine whether the relation \(R\) represented by the matrix is a partial order.[3]
  10. The relation itself is called a "partial order.[4]
  11. The word partial in the names "partial order" and "partially ordered set" is used as an indication that not every pair of elements needs to be comparable.[4]
  12. A set with a partial order is called a partially ordered set (also called a poset).[4]
  13. In some contexts, the partial order defined above is called a non-strict (or reflexive) partial order.[4]
  14. For a partial order, the size of the longest chain (antichain) is called the partial order length (partial order width).[5]
  15. A partial order, being a relation, can be represented by a di-graph.[6]
  16. Furthermore if is in the partial order, then remove the edge .[6]
  17. This packages provides the PartialOrd typeclass suitable for types admitting a partial order.[7]
  18. Provide a means for traversing through the partial order in a regular manner ( e .[8]
  19. Here \(w \le n\) is the width of the partial-order–a natural obstacle in searching a partial order.[9]
  20. Partial order There are two kinds of partial orders we can define - weak and strong.[10]
  21. The weak partial order is the more common one, so let's start with that.[10]
  22. Whenever I'm saying just "partial order", I'll mean a weak partial order.[10]
  23. The operator < on numbers is an example of strict partial order, since it satisfies all the properties; while \le is reflexive, < is irreflexive.[10]
  24. In this article, we define partial order relations on classifiers and families of classifiers, based on rankings of rate function values and rankings of test function values, respectively.[11]
  25. Each partial order relation provides a sufficient condition, which yields better classification error rates or better performance on the receiver operating characteristic analysis.[11]

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