* Completeness – all actions can be ranked in an order of preference ( indifference between two or more is possible ).

Completeness states that all true sentences are provable.

The Completeness theorem establishes an equivalence in first-order logic, between the formal provability of a formula, and its truth in all possible models.

* Completeness: all pa consequences are demonstrable from the initials ( T17 ).

* Completeness ; the degree to which all necessary concepts of the application domain are represented in the way of modeling.

* Completeness checks-controls that ensure all records were processed from initiation to completion.

# Completeness: the budget must include all instances of revenues and expenditures separately.

* Completeness: if the statement is true, the honest verifier ( that is, one following the protocol properly ) will be convinced of this fact by an honest prover.

# Completeness: if the statement is true, the honest verifier ( that is, one following the protocol properly ) will be convinced of this fact by an honest prover.

Completeness can be sacrificed in favor of any other quality.

Completeness here means that a deterministic Turing machine using only logarithmic space can transform any other problem in NL into an equivalent 2-satisfiability problem.

* Completeness: if the string is in the language, the prover must be able to give a certificate such that the verifier will accept with probability at least 2 / 3 ( depending on the verifier's random choices ).

Completeness seems to be at the center of shalom as we will see in the meaning of the term itself, in some derivatives from its root, shalam, in some examples of its uses in Jewish and Christian Scriptures, and in some homophone terms from other Semitic languages.

" The Gelukpa allow that it is possible to take the mind itself as the object of meditation, however, Zahler reports, the Gelukpa discourage it with " what seems to be thinly disguised sectarian polemics against the Nyingma Great Completeness and Kagyu Great Seal meditations.

It says that one who hears its reading will attain Ultimate Completeness, and one who abuses it will be sentenced to Hell.

Completeness of first-order logic was first explicitly established by Gödel, though some of the main results were contained in earlier work of Skolem.

Completeness and accuracy is described by the weakest apparent magnitude V ( largest number ) and the accuracy of the positions.

Completeness and accuracy of recall in the diffusion of the news from a newspaper vs a television source.

Two of Kripke's earlier works, A Completeness Theorem in Modal Logic and Semantical Considerations on Modal Logic, the former written while he was still a teenager, were on the subject of modal logic.

" A Completeness Theorem in Modal Logic ", Journal of Symbolic Logic 24 ( 1 ): 1 – 14.

" Another Approach: The Church-Turing ' Thesis ' as a Special Corollary of Gödel's Completeness Theorem ," in Computability: Gödel, Turing, Church, and beyond, Copeland, B. J., Posy, C., and Shagrir, O.

# Completeness: any statement is either provable or refutable ( i. e. its negation is provable ).

The word Dzogchen has been translated variously as Great Perfection, Great Completeness, Total Completeness, and Supercompleteness.

; Completeness: The design must cover as many important situations as is practical.

; Completeness: The design must cover as many important situations as is practical.

* Lawrence Solum, Default Rules and Completeness, Legal Theory Lexicon.

* Lawrence Solum, Default Rules and Completeness, Legal Theory Lexicon.

* ( Completeness ) Every universally valid second-order formula, under standard semantics, is provable.

" The Completeness of the First-Order Functional Calculus ", Journal of Symbolic Logic.

" Completeness in the theory of types ", Journal of Symbolic Logic 15: 81 – 91.

Completeness of the market is also important because in an incomplete market there are a multitude of possible prices for an asset corresponding to different risk-neutral measures.

A credulousness, a distaste for documentation, an uncritical reliance on contemporary accounts, and a proneness to assume a theory as true before adequate proof was provided were all evidences of his failure to comprehend the use of the scientific method or to evaluate the responsibilities of the historian to his reading public.

But I had the proof, all documented in a legal agreement which I would show her the moment I was free to do so.

( A formal proof for all finite sets would use the principle of mathematical induction to prove " for every natural number k, every family of k nonempty sets has a choice function.

Similarly, all the statements listed below which require choice or some weaker version thereof for their proof are unprovable in ZF, but since each is provable in ZF plus the axiom of choice, there are models of ZF in which each statement is true.

The proof of the independence result also shows that a wide class of mathematical statements, including all statements that can be phrased in the language of Peano arithmetic, are provable in ZF if and only if they are provable in ZFC.

A more general binomial theorem and the so-called " Pascal's triangle " were known in the 10th-century A. D. to Indian mathematician Halayudha and Persian mathematician Al-Karaji, in the 11th century to Persian poet and mathematician Omar Khayyam, and in the 13th century to Chinese mathematician Yang Hui, who all derived similar results .< ref > Al-Karaji also provided a mathematical proof of both the binomial theorem and Pascal's triangle, using mathematical induction.

And a single programmer could do most or all of the computer programming needed to generate the proof of concept to launch a new " killer " application.

In these memoirs, he paints himself as a born comedian, careless, light-hearted and with a happy temperament, proof against all strokes of fate, yet thoroughly respectable and honorable.

Noting another proof that self-replicating machines are possible is the simple fact that all living organisms are self replicating by definition.

Daniel Gorenstein announced in 1983 that the finite simple groups had all been classified, but this was premature as he had been misinformed about the proof of the classification of quasithin groups.

At the last moment, when his immense work was drawing to an end, he encountered a crowning mortification: he discovered that the bookseller, fearing the government's displeasure, had struck out from the proof sheets, after they had left Diderot's hands, all passages that he considered too dangerous.

For all his successes, the nature of his proof stirred up more trouble than Hilbert could have imagined at the time.

Various other speculative proposals have been made in the 19th and 20th centuries, all of them failing to gain significant acceptance because no significant proof of this connection was found.

In fact, the same proof shows that Euler's formula is even valid for all complex numbers z.

In response to Haeckel ’ s evolutionary claim that all vertebrates are essentially identical in the first month of embryonic life as proof of common descent, His responds by insisting that a more skilled observer would recognize even sooner that early embryos can be distinguished.

Initially, their proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand.

More precisely, all known FFT algorithms require Θ ( N log N ) operations ( technically, O only denotes an upper bound ), although there is no known proof that better complexity is impossible.

From these hypotheses, it is also possible to prove that there is only one God in each world by Leibniz's law, the identity of indiscernibles: two or more objects are identical ( are one and the same ) if they have all their properties in common, and so, there would only be one object in each world that possesses property G. Gödel did not attempt to do so however, as he purposely limited his proof to the issue of existence, rather than uniqueness.

Despite multiple parliamentary questions from as early as 2005, where it was stated that there was no proof that this was happening, Minister Ahern announced a ban on all handguns in November 2008.

The version given below attempts to represent all the steps in the proof and all the important ideas faithfully, while restating the proof in the modern language of mathematical logic.

Any of the several well-known axiomatisations will do ; we assume without proof all the basic well-known results about our formalism ( such as the normal form theorem or the soundness theorem ) that we need.