Sentence examples for orderable set from inspiring English sources

We now show that S ( x ) is a countably orderable set by a relation r ⊂ X × X.

Let X be a countably orderable set by a relation s ⊂ X × X. Assume that for any sequence ( x i ) ⊂ X satisfying x i s x i + 1 for all i ∈ N. there are a subsequence ( x i k ) ⊂ ( x i ) and an element x such that x i k s x for all k ∈ N. Then an s ∗ -maximal element of X exists.

The new metric, specifically designed to quantify conflict on orderable sets, uses a Hausdorff-based measure to account for the distance between focal elements.

Providers interact with a Java-based desktop client (Java version 1.42.09) that queries an Oracle 10 database (Oracle Corporation, Redwood Shores, CA) holding both the clinical content tables (e.g., orderables, order sets, and clinical decision support information) and patient information tables (e.g., patient identity, care area, diagnoses, existing orders).

In Cantor's notation, the continuum hypothesis can be stated by the simple equation 2ℵ0 = ℵ1, where ℵ0 is the cardinal number of an infinite countable set (such as the set of natural numbers), and the cardinal numbers of larger "well-orderable sets" are ℵ1, ℵ2, …, ℵα, …, indexed by the ordinal numbers.

Recall that a group is called right orderable if there is a linear order on the set of its elements invariant with respect to multiplication on the right.

Second, the set of all clusters must be orderable consistently with sequence orders of their residues.

A group is bi-orderable (or totally orderable) if there is a linear order invariant with respect to multiplication on the left and on the right.

A set X with a relation s ⊂ X × X is countably orderable with respect to s if for every nonempty subset W ⊆ X there exists a well-ordered relation μ on W such that v μ w ⇒ v s ∗ w for every  v, w ∈ W, v ≠ w. implies that W is at most countable.

In this example it is observable that there are loops of connections where the contigs are almost uniquely orderable but there also occur parts where such a linear order can not be achieved.

Despite Zermelo's endorsement here, the correctness of the hypothesis that the scale of aleph numbers represents all cardinals (AH, for short) is a more complicated matter, for it involves the claim that every set is actually equivalent to an initial segment of the ordinals, and not just well-orderable.