Informally speaking, the prime number theorem states that if a random integer is selected in the range of zero to some large integer N, the probability that the selected integer is prime is about 1 / ln ( N ), where ln ( N ) is the natural logarithm of N. For example, among the positive integers up to and including N = 10 < sup > 3 </ sup > about one in seven numbers is prime, whereas up to and including N = 10 < sup > 10 </ sup > about one in 23 numbers is prime ( where ln ( 10 < sup > 3 </ sup >)= 6. 90775528. and ln ( 10 < sup > 10 </ sup >)= 23. 0258509 ).

Informally, a set of natural numbers A is Turing reducible to a set B if there is an oracle machine that correctly tells whether numbers are in A when run with B as the oracle set ( in this case, the set A is also said to be ( relatively ) computable from B and recursive in B ).

Informally, the reason is that the memory of such a language is limited.

Informally, a language L is in MA if for all strings in the language, there is a polynomial sized proof that Merlin can send Arthur to convince him of this fact with high probability, and for all strings not in the language there is no proof that convinces Arthur with high probability.

Informally, and using programming language jargon, a tree ( xy ) can be thought of as a " function " x applied to an

Informally, the creole is known by the term dialect, as the creole is often perceived by locals as a dialect variety of English instead of an English creole language.

Informally, it says that all sufficiently long words in a regular language may be pumped — that is, have a middle section of the word repeated an arbitrary number of times — to produce a new word which also lies within the same language.

Such a definition can be formulated in terms of equivalence classes of smooth functions on M. Informally, we will say that two smooth functions f and g are equivalent at a point x if they have the same first-order behavior near x.

Informally, in attempting to estimate the causal effect of some variable x on another y, an instrument is a third variable z which affects y only through its effect on x.

Informally, one might say that the Dirac string carries away the " excess curvature " that would otherwise prevent F from being a closed form, as one has that everywhere except at the location of the monopole.

Informally, many Mechlinians ( in Dutch Mechelaars and locally pronounced Mecheleirs, people from this city ) daily speak Mechlinian ( in Dutch as well as locally Mechels ), a dialect by Dutch-speakers of Belgium pin-pointingly distincted from other Brabantic dialects by three different vowels of Dutch ( as in zout or rauw, in kei or bijl, in nu ) being typically pronounced as a same vowel – close to the one in English ' raw ' which does not appear in other dialects of the Flemish Region or in standard Dutch.

Informally, classes are also traditionally named after their lead ships.

Informally representing the interests of the Reich government abroad, Cuno rejected several proposals to assume the post of foreign minister, but agreed to form the Cabinet after the resignation of Joseph Wirth.

Informally the island was used by fishermen from Cuba and from the British Bahamas, who were later joined by others from the United States after the latter nation's independence.

Informally known as " Friends ' Central ," the school encompasses three divisions: lower school ( nursery through 4th grades ), middle school ( 5th through 8th ) and upper school ( 9th through 12th ).

Informally, the " P vs. NP " question asks whether every optimization problem whose answers can be efficiently verified for correctness / optimality can be solved optimally with an efficient algorithm.

Informally, if P is any polyhedron or polytope, and tP is the polytope formed by expanding P by a factor of t in each dimension, then L ( int P, t ) is the number of integer lattice points in tP.

Informally the Church – Turing thesis states that if some method ( algorithm ) exists to carry out a calculation, then the same calculation can also be carried out by a Turing machine ( as well as by a recursively definable function, and by a λ-function ).

Informally, word formation rules form " new words " ( that is, new lexemes ), while inflection rules yield variant forms of the " same " word ( lexeme ).

Informally, Chantilly is located around the intersection of US-50 ( Lee Jackson Memorial Hwy ) and VA-28 ( Sully Rd ).

Informally, the tangent bundle of a manifold ( in this case a circle ) is obtained by considering all the tangent spaces ( top ), and joining them together in a smooth and non-overlapping manner ( bottom ).

Informally, given the prime factorization of m, take b to be the product of the prime factors of m that have an odd exponent ( if there are none, then take b to be 1 ).

Informally, a path expression is a sequence of steps separated by the "" operator, for example ( which is short for ).

Informally, many older Lossos stated that the Nawdba came " from the East, toward Djougou ( in Bénin ).

Informally: a formula in prenex form containing existential quantifiers only is provable ( valid ) in first-order logic if and only if a disjunction composed of substitution instances of the quantifier-free subformula of is a tautology ( propositionally derivable ).

After the seventeenth century the audience ceased to be an organic community to which these ideas and their attendant habits of figurative language would be natural or immediately familiar.

Pseudocode, flowcharts and control tables are structured ways to express algorithms that avoid many of the ambiguities common in natural language statements.

Steiner believed results of this form of spiritual research should be expressed in a way that can be understood and evaluated on the same basis as the results of natural science: " The anthroposophical schooling of thinking leads to the development of a non-sensory, or so-called supersensory consciousness, whereby the spiritual researcher brings the experiences of this realm into ideas, concepts, and expressive language in a form which people can understand who do not yet have the capacity to achieve the supersensory experiences necessary for individual research.

In 1929, Mojżesz Presburger showed that the theory of natural numbers with addition and equality ( now called Presburger arithmetic in his honor ) is decidable and gave an algorithm that could determine if a given sentence in the language was true or false.

In this noble prayer are evinced profound religious feeling and exalted thought, as well as ability to use the Hebrew language in a natural, expressive, and classical manner ( Jerusalem Talmud Rosh Hashanah i. 57a ).

AI-complete problems are hypothesised to include computer vision, natural language understanding, and dealing with unexpected circumstances while solving any real world problem.

But Sapir had since become influenced by a current of logical positivism, such as that of Bertrand Russel and the early Ludwig Wittgenstein, particularly through Ogden and Richards ' The Meaning of Meaning, from which he adopted the a view that natural language potentially obscures, rather than facilitates, the mind to perceive and describe the world as it really is.

Moreover, like all natural language based IALs, Basic is subject to criticism as unfairly biased towards the native speaker community.

In the sense of this article, a naive theory is a non-formalized theory, that is, a theory that uses a natural language to describe sets.

In a simple model, often referred to as the transmission model or standard view of communication, information or content ( e. g. a message in natural language ) is sent in some form ( as spoken language ) from an emisor / sender / encoder to a destination / receiver / decoder.

This source code is written in a programming language, which is an artificial language often more restrictive or demanding than natural languages, but easily translated by the computer.

It is usually written in high-level programming languages that are easier and more efficient for humans to use ( closer to natural language ) than machine language.

Software may also be written in an assembly language, essentially, a mnemonic representation of a machine language using a natural language alphabet.

Computational linguistics is an interdisciplinary field dealing with the statistical or rule-based modeling of natural language from a computational perspective.

Traditionally, computational linguistics was usually performed by computer scientists who had specialized in the application of computers to the processing of a natural language.

The concept of context-sensitive grammar was introduced by Noam Chomsky in the 1950s as a way to describe the syntax of natural language where it is indeed often the case that a word may or may not be appropriate in a certain place depending upon the context.

Context-free grammars are important in linguistics for describing the structure of sentences and words in natural language, and in computer science for describing the structure of programming languages and other formal languages.

A context-free grammar provides a simple and mathematically precise mechanism for describing the methods by which phrases in some natural language are built from smaller blocks, capturing the " block structure " of sentences in a natural way.

Important features of natural language syntax such as agreement and reference are not part of the context-free grammar, but the basic recursive structure of sentences, the way in which clauses nest inside other clauses, and the way in which lists of adjectives and adverbs are swallowed by nouns and verbs, is described exactly.