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{{Split|date=May 2013}}
{{Wiktionary|completeness}}
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==<!-- [[Completeness (logic)]] redirects here -->
In [[logic]], semantic completeness is the [[Conversion (logic)|converse]] of [[soundness]] for [[formal systems]]. A formal system is "semantically complete" when all its [[tautology (logic)|tautologies]] are [[theorem]]s, 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 [[consistency|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 {{mathcal|S}} is '''semantically complete''' or simply '''complete''', if every tautology of {{mathcal|S}} is a theorem of {{mathcal|S}}. That is, <math> \models_{\mathcal S} \varphi\ \to\ \vdash_{\mathcal S} \varphi</math>.<ref name="metalogic">Hunter, Geoffrey, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Pres, 1971</ref>
 
*A formal system {{mathcal|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, <math> \Gamma\models_{\mathcal S} \varphi \ \to\ \Gamma \vdash_{\mathcal S} \varphi</math>.
 
*A formal system {{mathcal|S}} is '''syntactically complete''' or '''deductively complete''' or '''maximally complete''' or simply '''complete''' if for each [[Sentence (mathematical logic)|sentence]] (closed formula) φ of the language of the system either φ or ¬φ is a theorem of {{mathcal|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 system of [[logical connective]]s is [[functional completeness|functionally complete]] if and only if it can express all [[propositional function]]s.
 
*A language is '''expressively complete''' if it can express the subject matter for which it is intended.{{Citation needed|date=December 2008}}
 
*A formal system is '''complete with respect to a property''' if and only if every sentence that has the [[property (philosophy)|property]] is a theorem.{{Citation needed|date=December 2008}}
 
==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 (mathematics)|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).
 
* A [[metric space]] is ''complete'' if every [[Cauchy sequence]] in  it [[limit of a sequence|converges]]. See [[Complete metric space]].
 
* A [[uniform space]] is ''complete'' if every [[Cauchy net]] in  it [[Net (mathematics)#Limits of nets|converges]] (or equivalently every [[Cauchy filter]] in it [[Filter (mathematics)#Convergent filter bases|converges]]).
 
* In [[functional analysis]], a [[subset]] ''S'' of a [[topological vector space]] ''V'' is ''complete'' if its [[span (linear algebra)|span]] is [[dense (topology)|dense]] in ''V''. In the particular case of [[Hilbert space]]s (or more generally, [[inner product space]]s), an [[orthonormal basis]] is a set that is both complete and [[orthonormal]].
 
* A [[measure (mathematics)|measure space]] is ''complete'' if every subset of every [[null set]] is measurable. See [[complete measure]].
 
* In [[commutative algebra]], a commutative ring can be completed at an ideal (in the topology defined by the powers of the ideal). See [[Completion (ring theory)]].
 
* More generally, any [[topological group]] can be completed at a decreasing sequence of open subgroups.
 
* In [[statistics]], a [[statistic]] is called ''complete'' if it does not allow an unbiased estimator of zero. See [[completeness (statistics)]].
 
* In [[graph theory]], a ''[[complete graph]]'' is an undirected graph in which every pair of vertices has exactly one edge connecting them.
 
* In [[category theory]], a category ''C'' is ''[[complete category|complete]]'' if every [[diagram (category theory)|diagram]] from a small category to ''C'' has a [[limit (category theory)|limit]]; it is ''[[cocomplete]]'' if every such functor has a [[colimit]].
 
* In [[order theory]] and related fields such as [[lattice (order)|lattice]] and [[domain theory]], ''[[completeness (order theory)|completeness]]'' generally refers to the existence of certain [[supremum|suprema]] or [[infimum|infima]] of some [[partially ordered set]]. Notable special usages of the term include the concepts of [[complete Boolean algebra]], [[complete lattice]], and [[complete partial order]] (cpo). Furthermore, an [[ordered field]] is ''complete'' if every non-empty subset of it that has an upper bound within the field has a [[least upper bound]] within the field, which should be compared to the (slightly different) order-theoretical notion of [[bounded complete]]ness. [[Up to]] [[isomorphism]] there is only one complete ordered field: the field of [[real number]]s (but note that this complete ordered field, which is also a lattice, is not a complete lattice).
 
* In [[algebraic geometry]], an [[algebraic variety]] is ''complete'' if it satisfies an analog of [[compact space|compactness]].  See [[complete algebraic variety]].
 
* In [[quantum mechanics]], a [[complete set of commuting operators]] (or CSCO) is one whose [[eigenvalues]] are sufficient to specify the physical state of a system.
 
== 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 (complexity)|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.<br>For example, each problem in the class '''[[NP-complete]]''' is complete for the class '''[[NP (complexity)|NP]]''', under [[polynomial time|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 (knowledge bases)|completeness]] is found in [[knowledge base]] theory.
 
==Economics, finance, and industry==
* [[Complete market]]s 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 (oil and gas wells)|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 ==
 
{{reflist}}
 
{{logic}}
 
[[Category:Mathematical terminology]]
[[Category:Mathematical logic]]
[[Category:Proof theory]]
[[Category:Metalogic]]
 
[[hr:Potpunost (razdvojba)]]
[[ja:完全性]]
[[pl:Zupełność]]
[[zh:完備性]]

Revision as of 02:45, 25 February 2014

Simple And Advanced Residence Enhancement Methods

Today, possessing outside lights is an crucial part of our residences. If we care about the interior areas of our house Saleh Stevens , we should exhibit a lot more about its exterior as effectively. 1 way of creating our home seem good is to install outdoors lighting arrangements.

This is the sort of organization that you can trust to give you the ideal mend solutions that you actually require. It is vey crucial that you also get keep of the greatest for you to get the ideal fix Saleh Stevens that you can constantly trust. It is anything that every particular person who has skilled any electrical difficulty want.

The panels will be prepared constructed, and you get the recommendations and all the parts. Then it is a method of placing it all with each other. If you want everything to function out correct, then this is the ideal strategy.

Such out of doors lanterns are rather easy to established up and wire. Some even will come pre-wired at your ease. Even so, if you want different combinations of pole and lanterns, you may have to do the wiring by yourself. You will also need to do some digging to keep the wires buried underground. If it all appears a bit mind-boggling for you, it is advised to employ the service of the aid of a skilled Saleh Stevens to be sure that the wirings are risk-free.

A Marketer need to have a internet web site or a blog to generate a presence on the world wide web. He or she need to also have an auto responder and other necessary instruments needed to construct the business. A marketer must also have the education necessary to marketplace products and companies.

You can get wonderful looking photo voltaic backyard garden stakes in the designs of butterflies, dragonflies, hummingbirds, orbs and a great deal of others and in so several shades. Envision your garden coming alive at night time with these small fellas glowing all above your yard. There are a wonderful a lot of that will also modify shades intermittently so your yard doesn't search Saleh Stevens the exact same from a single instant to the following.

So, what is solar lights? It is the harnessing of the solar's light-weight and converting it into usable electrical power. Also called Photovoltaic Electricity Technology or PV. To really simplify it, a photo voltaic cell (PV gadget) collects and converts the sunlight into DC (immediate recent) which is utilized to electricity whatever the point is. Numerous of these photo voltaic cells make up a photo voltaic panel. The far more intensive the sunlight is, the more quickly the electrical energy flows. The best factor is, it is a pollution free of charge power supply and requires minor to no servicing as soon as put in.

Window Troubles- Windows are some of the much more frequently destroyed parts of properties, largely in relationship with its glass. Wooden body home windows expense more to change so you should go doe metal ones if you want less maintenance.

This is one particular of the very best places to get that trustworthy support. Therefore, electrician Tacoma will give you the electrical restore services that you need to have. If you have any other electrical problem, you can seek out advice of seek advice from with the authorities and you will locate an amicable remedy to it all. It is something that you can completely have confidence in for usefulness. You only need to have to know that the best is there for you. You can have confidence in the company to offer you the very best answer to your electrical seattle difficulties.