Sentence examples for ordered relation from inspiring English sources

Let X be an ordered Hilbert space and ≤ be a partially ordered relation.

Define an ordered relation ≤ on X by x ≤ y iff  x ( t ) ≤ y ( t ), ∀ t ∈ [ 0, T ].

The real Banach space X endowed with the ordered relation ≤ defined by C is called an ordered real Banach space.

A series of this type is clearly neither open nor infinite, since if it were there would no longer be an ordered relation between the terms.

Then Ω is an Ω-distance on X.Define an ordered relation ≤ on X by x ≤ y iff x ( t ) ≤ y ( t ), ∀ t ∈ [ 0, 1 ].

Let X be a real ordered Banach space with a norm ∥ ⋅ ∥, a normal cone P and a partial ordered relation ≤ defined by the cone P, for arbitrary x, y ∈ X, lub { x, y } and glb { x, y } express the least upper bound of the set { x, y } and the greatest lower bound of the set { x, y } on the partial ordered relation ≤, respectively.

(Note that the ordering relation is not symmetric).

The ordering relation "less than or equal to" (symbolized by ≤) is reflexive, but "less than" (symbolized by <) is not.

Nieuwentijdt postulates a domain of quantities, or numbers, subject to a ordering relation of greater or less.

We define the ordering relations as follows.

The second major difficulty is along the same lines, concerning, not functions, but relations, and thus ordering relations and ordinal numbers.