Sentence examples for ordered field from inspiring English sources

Then, we put together a conceptual framework that situates modes of governance into an ordered field.

In September, LAPD brass ordered field officers to carry the devices on their holsters unless they weren't available.

Suppose that, by analogy, we start from our second-order axiomatization of the ordered field of real numbers, and replace the second-order least-upper-bound axiom by the corresponding schema.

One of our methods then reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can be solved using computational logic packages.

Where ρ 0, 1, +, ×, <) is the second-order sentence that characterizes the ordered field of real numbers up to isomorphism, the sentence ∃x ∃y ∃F ∃G ∃R ρ x, y, F, G, R) is a sentence in the second-order language of equality that is true in the power of the continuum and in no other cardinality.

Noteworthy here are two aspects: Not only does he accept this system as an "actual infinity", in the sense of a complete infinite set that is treated as a mathematical object in itself; he also considers it "structurally", as an example of a linearly ordered set closed under addition and multiplication (an ordered field).

The models of this are called real-closed ordered fields.

To use modern terminology, Peirce was claiming to have shown the existence of ordered fields that were non-Archimedean.

Most of the value metrics in primary care are still input-based: procedures performed, tests ordered, fields filled in the electronic health record.

The F.B.I. is ordering field supervisors to count the number of mosques and Muslims in their areas as part of the antiterrorism effort.

Instead, the Navy will order field commanders to hold disciplinary reviews for the officers involved, which is the Navy's standard procedure in such cases.