completeness condition

USAGE SUMMARY

The phrase "completeness condition" is correct and usable in written English.
It can be used in contexts related to mathematics, logic, or computer science, where it refers to a requirement that ensures a system or theory is complete. Example: "In order to validate the theorem, we must check if it satisfies the completeness condition."

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

8 human-written examples

For example, the sentence "Jenny knows who left" has two conditions: a Completeness condition, that Jenny knows an answer that completely addresses the question "who left", and a false answer (FA- sensitivity condition, that Jenny has no FA- sensitivitylevant to "who left".

University of Chicago

We proved also that our proximal orbital completeness condition is weaker than the compactness condition and the proximal condition of second kind.

Fixed Point Theory and Applications

To satisfy the completeness condition, that all Cauchy sequences of functions converge (in the mean) to some function in that space, he specified that integration must be defined in the manner of Lebesgue.

SEP

The completeness condition requires that there are no further disturbing factors i.e., it requires an exclusive cp-clause (see section 3) Canfield and Lehrer also present an argument for why these cp-clauses cannot be defined away (any such attempt leads to an infinite regress of further cp-clauses).

SEP

We note ({|alpha,irangle }) the eigenbasis constructed from the eigenstates of (H_{mathrm{mat}}^{alpha}) that satisfied (H_{mathrm{mat}}|alpha,irangle = E^{alpha}_{i} |irangle ) and the completeness condition (sum_{i} |alpha, irangle langle alpha,i| = I_{d}^{alpha}), where (I_{d}^{alpha}) is the identity matrix acting on the subspace of the (alpha^{th}) emitter.

EPJ Quantum Technology

Applying twice the completeness condition on the Hamiltonian (H_{mathrm{mat}}^{alpha}), one finds (H_{mathrm{mat}}^{alpha} = frac {E_+E_{2}I_{d}^{alpha} + frac{hbaromega^{alpha}}{2} sigma ^{alpha}_{z} ) where (hbaromega^{alpha} = E_^{alpha} - E_^{alpha}) and (sigma_{z}^{alpha} = |alpha,+rangle langle alpha,+| - |alpha,-rangle langle alpha,-|).

EPJ Quantum Technology

Human-verified similar examples from authoritative sources

Similar Expressions

52 human-written examples

This process also clearly establishes consistency and completeness conditions.

Advances in Engineering Software

Using this notion, they established best proximity point theorems under some mild conditions; indeed, their hypotheses were a combination of compactness and completeness conditions.

Fixed Point Theory and Applications

In [15] and [16], Li and the first author have shown that the affine Kähler-Ricci flat graph hypersurface has a rigidity property under different completeness conditions.

Journal of Inequalities and Applications

In the following theorem, the chain-completeness condition for the underlying space is replaced by the chain-completeness property of the range of the considered mapping, where the range of a set-valued mapping (F: P rightarrow 2^{P}backslash{emptyset}) is defined as F(P) = bigcup bigl{ F x): x in Pbigr}.

Fixed Point Theory and Applications

Which is why getting your hands on a real first edition in parts of, say, "David Copperfield" will run you about $12,500, depending on its completeness and condition.

Los Angeles Times

Expert writing Tips

Best practice

When discussing mathematical or logical systems, clearly define what constitutes "completeness" within that specific context to avoid ambiguity. For instance, in propositional logic, completeness means that every valid formula is provable.

Common error

Avoid using "completeness condition" when you actually mean soundness. Completeness implies that all true statements can be proven, whereas soundness means that all provable statements are true. Misunderstanding this distinction can lead to logical errors.

Linguistic Context

The phrase "completeness condition" functions as a technical term specifying a criterion or requirement for a system or theory to be considered complete. Ludwig AI, as exemplified by the provided examples, shows that it often appears in academic and scientific contexts.

Expression frequency: Uncommon

Frequent in

Science

60%

Academia

30%

News & Media

10%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "completeness condition" is a technical term mainly used in scientific and academic contexts to describe a necessary criterion for a system or theory to be considered complete. As Ludwig AI shows, it emphasizes a requirement ensuring all possible elements or solutions within a given space are accounted for. It is crucial to distinguish it from related concepts like soundness. Alternatives such as "sufficiency requirement" can be used depending on the specific nuance. The phrase is grammatically correct and its usage frequency is uncommon.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

sufficiency requirement

Emphasizes the need for enough elements to satisfy a criterion.

totality constraint

Focuses on ensuring all possible cases are covered.

integrity rule

Highlights the maintenance of data or system integrity.

closure property

Describes a set's characteristic of containing all results of an operation.

exhaustive criterion

Implies a criterion that covers every possibility without exception.

all-encompassing requirement

Stresses the comprehensiveness of the required condition.

universal prerequisite

Suggests a necessary condition applicable in all instances.

global provision

Indicates a rule or condition that is broadly applicable.

comprehensive specification

Implies a detailed and thorough set of conditions.

absolute necessity

Underscores the indispensable nature of the condition.

FAQs

How is "completeness condition" used in mathematics?

In mathematics, a "completeness condition" often refers to a requirement ensuring that all possible solutions or elements within a given space are accounted for. For example, a complete metric space ensures that all Cauchy sequences converge within that space.

What does a "completeness condition" mean in logic?

In logic, the "completeness condition" ensures that every valid argument can be proven within the system. This is distinct from soundness, which requires that every provable argument is valid.

Can I use alternatives to "completeness condition"?

Yes, depending on the context, you can use alternatives like "sufficiency requirement", "totality constraint", or "exhaustive criterion". The best choice depends on the specific nuance you want to convey.

How does the "completeness condition" relate to physicalism?

In philosophy, specifically regarding physicalism, the "completeness condition" addresses whether physical facts fully determine all facts. It's a central question in debates about the scope and limits of physical explanations.