digplanet beta 1: Athena
Share digplanet:

Agriculture

Applied sciences

Arts

Belief

Chronology

Culture

Education

Environment

Geography

Health

History

Humanities

Language

Law

Life

Mathematics

Nature

People

Politics

Science

Society

Technology

In general, an object is complete if nothing needs to be added to it. This notion is made more specific in various fields.

## Logical completeness

In logic, semantic completeness is the converse of soundness for formal systems. A formal system is "semantically complete" when all its tautologies are theorems, whereas a formal system is "sound" when all theorems are tautologies (that is, they are semantically valid formulas: formulas that are true under every interpretation of the language of the system that is consistent with the rules of the system). Kurt Gödel, Leon Henkin, and Emil Post all published proofs of completeness. (See History of the Church–Turing thesis.) A formal system is consistent if for all formulas φ of the system, the formulas φ and ¬φ (the negation of φ) are not both theorems of the system (that is, they cannot be both proved with the rules of the system).

• A formal system S is semantically complete or simply complete, if every tautology of S is a theorem of S. That is, $\models_{\mathcal S} \varphi\ \to\ \vdash_{\mathcal S} \varphi$.[1]
• A formal system S is strongly complete or complete in the strong sense if for every set of premises Γ, any formula which semantically follows from Γ is derivable from Γ. That is, $\Gamma\models_{\mathcal S} \varphi \ \to\ \Gamma \vdash_{\mathcal S} \varphi$.
• A formal system S is syntactically complete or deductively complete or maximally complete or simply complete if for each sentence (closed formula) φ of the language of the system either φ or ¬φ is a theorem of S. This is also called negation completeness. In another sense, a formal system is syntactically complete if and only if no unprovable axiom can be added to it as an axiom without introducing an inconsistency. Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example, the propositional logic statement consisting of a single propositional variable A is not a theorem, and neither is its negation, but these are not tautologies). Gödel's incompleteness theorem shows that any recursive system that is sufficiently powerful, such as Peano arithmetic, cannot be both consistent and syntactically complete.
• A language is expressively complete if it can express the subject matter for which it is intended.[citation needed]
• A formal system is complete with respect to a property if and only if every sentence that has the property is a theorem.[citation needed]

## Mathematical completeness

In mathematics, "complete" is a term that takes on specific meanings in specific situations, and not every situation in which a type of "completion" occurs is called a "completion". See, for example, algebraically closed field or compactification.

• The completeness of the real numbers is one of the defining properties of the real number system. It may be described equivalently as either the completeness of R as metric space or as a partially ordered set (see below).
• More generally, any topological group can be completed at a decreasing sequence of open subgroups.

## Computing

• In algorithms, the notion of completeness refers to the ability of the algorithm to find a solution if one exists, and if not, to report that no solution is possible.
• In computational complexity theory, a problem P is complete for a complexity class C, under a given type of reduction, if P is in C, and every problem in C reduces to P using that reduction.
For example, each problem in the class NP-complete is complete for the class NP, under polynomial-time, many-one reduction.
• In computing, a data-entry field can autocomplete the entered data based on the prefix typed into the field; that capability is known as autocompletion.
• In software testing, completeness has for goal the functional verification of call graph (between software item) and control graph (inside each software item).
• The concept of completeness is found in knowledge base theory.

## Economics, finance, and industry

• Complete markets versus incomplete markets
• In auditing, completeness is one of the financial statement assertions that have to be ensured. For example, auditing classes of transactions. Rental expense which includes 12-month or 52-week payments should be all booked according to the terms agreed in the tenancy agreement.
• Oil or gas well completion, the process of making a well ready for production.

## Botany

• A complete flower is a flower with both male and female reproductive structures as well as petals and sepals. See Sexual reproduction in plants.

## References

1. ^ Hunter, Geoffrey, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Pres, 1971

Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Completeness — Please support Wikipedia.
A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.
 17151 videos foundNext >
 17151 videos foundNext >
 27845 news items
 Almirante: Completeness of service Sun.Star Fri, 17 May 2013 08:57:35 -0700 For completeness of service by registered mail, the reckoning period starts either (a) from the date of actual receipt of the mail by the addressee or (b) after five days from the date he received the first notice from the postmaster. There must be a ... Alcatel-Lucent Application Moves A Step Closer to Public Hearing Patch.com Wed, 22 May 2013 03:17:58 -0700 The Holmdel Planning Board approved application completeness waivers for Somerset Developers regarding the Alacatel-Lucent project, bringing it one step closer to an official public hearing. A completeness waiver, granted at the May 14 meeting, does ... Can Data Storage Ever Reach An Absolute Limit? Forbes Wed, 22 May 2013 08:09:48 -0700 For completeness's sake, I should mention electronic quantum holography. This uses a technique I won't pretend to understand to make an electron act like it has multiple wavelengths at the same time, allowing you to store 35 bits on a single electron! Salon “Original Coca-Cola had a very small amount of cocaine” Salon Wed, 22 May 2013 10:29:06 -0700 But the completeness of the company's history in this book paints a bigger picture, and Coca-Cola's tangles with death squads fit in as just one piece. This is a company devoted to, above all else, making as much money as possible and selling as much ... Real estate vs. stock market: Where to invest? NDTV Wed, 22 May 2013 08:34:54 -0700 Disclaimer: All information in this article has been provided by InvestmentYogi.com and NDTV Profit is not responsible for the accuracy and completeness of the same. Story first published on: May 22, 2013 20:35 (IST). Tags: Real estate, Stock markets, ... Bureau to probe forestry claims Taipei Times Wed, 22 May 2013 09:06:19 -0700 “Green Forestation” is one of the government's “i-Taiwan 12 Projects,” the environmental group said, adding that the project's goals include maintaining the completeness of the environment at nature reserves, providing space for the survival of plants ... Small, speedy plant-eater extends knowledge of dinosaur ecosystems EurekAlert (press release) Wed, 22 May 2013 10:19:23 -0700 IMAGE: Skeletal outlines illustrate both the relative size and completeness of two of the small ornithopod specimens described in the paper. Bones indicated in white are present. Human (in gray) for. Wall Street Fundamentals Releases New In-Depth Stock Reports on BLOX, FFIV ... Baystreet.ca Wed, 22 May 2013 11:09:52 -0700 Disclaimer: Information, opinions and analysis contained herein are based on sources believed to be reliable, but no representation, expressed or implied, is made as to its accuracy, completeness or correctness. The opinions contained herein reflect ...
 Limit to books that you can completely read online Include partial books (book previews) .gsc-branding { display:block; }

Oops, we seem to be having trouble contacting Twitter

You can talk about Completeness with people all over the world in our discussions.