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.

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.

Initially, BASIC concentrated on supporting straightforward mathematical work, with matrix arithmetic support from its initial implementation as a batch language and full string functionality being added by 1965.

Since computers can make arithmetic calculations much faster and more accurately than humans, it was thought to be only a short matter of time before the technical details could be taken care of that would allow them the same remarkable capacity to process language.

Rather, we say that a real a is definable in the language of arithmetic ( or arithmetical ) if its Dedekind cut can be defined as a predicate in that language ; that is, if there is a first-order formula φ in the language of arithmetic, with two free variables, such that

Sometimes " long double " is used for this in the C language family ( the C99 and C11 standards " IEC 60559 floating-point arithmetic extension-Annex F " recommend the 80-bit extended format to be provided as " long double " when available ), though " long double " may be a synonym for " double " or may stand for quadruple precision.

When considered over a countable language, the completeness and compactness theorems are equivalent to each other and equivalent to a weak form of choice known as weak König's lemma, with the equivalence provable in RCA < sub > 0 </ sub > ( a second-order variant of Peano arithmetic restricted to induction over Σ < sup > 0 </ sup >< sub style =" margin-left :- 0. 6em "> 1 </ sub > formulas ).

The language contains ordinary arithmetic and comparison operators, and unconditional, conditional, and assigned jumps.

Translation: Concept Script, a formal language of pure thought modelled upon that of arithmetic, by S. Bauer-Mengelberg in Jean Van Heijenoort, ed., 1967.

However, the spoken language uses both arithmetic and geometric numerals.

This means it is possible to effectively determine, for any sentence in the language of Presburger arithmetic, whether that sentence is provable from the axioms of Presburger arithmetic.

The language of Presburger arithmetic contains constants 0 and 1 and a binary function +, interpreted as addition.

In this language, the axioms of Presburger arithmetic are the universal closures of the following:

# Let P ( x ) be a first-order formula in the language of Presburger arithmetic with a free variable x ( and possibly other free variables ).

The Ambi programming language uses Polish Notation for arithmetic operations and program construction.

Gödel's first incompleteness theorem shows that for languages sufficient for doing a certain amount of arithmetic, there can be no effective deductive system that is complete with respect to the intended interpretation of the symbolism of that language.

The full complement of arithmetic and binary operators is defined on vector types so that the normal C expression language can be used to manipulate vector variables.

While the language provides simple matrix operations such as multiplication, the Scilab package also provides a library of high-level operations such as correlation and complex multidimensional arithmetic.

It might be pointed out that the integrating function of religion, for good or ill, has often supported or been identified with other groupings -- political, nationality, language, class, racial, sociability, even economic.

It has become painfully clear that the very attempt to make the language of social research free of values by erecting mathematical and physical models, is itself a conditioned response to a world which pays a premium price for technological manipulation.

aside from her specifically regional accent, she reveals by the use of the triad, `` irritable, tense, depressed '', a certain pedantic itemization that indicates she has some familiarity with literary or scientific language ( i.e., she must have had at least a high-school education ), and she is telling a story she has mentally rehearsed some time before.

Of the two, Porter is justly the better known, for he went far beyond the vital finding of fiction for films to take the first step toward fashioning a language of film, toward making the motion picture the intricate, efficient time machine that it has remained since, even in the most inept hands.

The complexities of communication have been considerably abetted in this case by appropriately stilted English language that has been excellently dubbed in place of the Russian dialogue.

In the former, the encounter with multiple, distinct cultures, often very different in organization and language from those of Europe, has led to a continuing emphasis on cross-cultural comparison and a receptiveness to certain kinds of cultural relativism.

Swift has his proposer further degrade the Irish by using language ordinarily reserved for animals.

A true alphabet has letters for the vowels of a language as well as the consonants.

Recently, Corey Anton has argued that we cannot be certain what is separate from or unified with something else: language, he asserts, divides what is not in fact separate.

Based on the proposed correspondences listed below, the following phoneme inventory has been reconstructed for the hypothetical Proto (- Macro )- Altaic language ( taken from Blažek's summary of the newest Altaic etymological dictionary et al.

It is a very traditional form of the language, probably derived from medieval deeds and documents, and has a very complicated structure and vocabulary which is generally reserved only for such documents.

Anatolia has been proposed to be the origin of the Indo-European language family.

The word " alphabet " in English has a source in Greek language in which the first two letters were " A " ( alpha ) and " B " ( beta ), hence " alphabeta ".

The use of a single official language, which modern scholarship has dubbed Official Aramaic or Imperial Aramaic, can be assumed to have greatly contributed to the astonishing success of the Achaemenids in holding their far-flung empire together for as long as they did.

As a language of deaf education, ASL has been introduced to numerous countries, where it has often diverged into a separate dialect.

In recent years, researchers have shown that exposure to sign language has a positive impact on the socialization of hearing children.

ASL has come a long way from its condemned days of banned use to being viewed as a grammatical language, which is the main form of communication in American Deaf culture.

The French word artiste ( which in French, simply means " artist ") has been imported into the English language where it means a performer ( frequently in Music Hall or Vaudeville ).

His advice has remained in the English language as the saying, " When in Rome, do as the Romans do.

Today, it is estimated that fewer than 100 speakers of the language remain, while other research places the number at fewer than 15 speakers – the language has been regarded as “ endangered ”.

In fact, no attempt to show a relationship with Ainu to any other language has gained wide acceptance, and Ainu is currently considered to be a language isolate.

A `` mental image '' subconsciously impressing us from beneath its language symbols in wakeful thought, or consciously in light sleep, is actually not an image at all but is comprised of realities, viewed not in the concurrent sensory stream, but within the depths of the fourth dimension.

Cultural anthropology also covers economic and political organization, law and conflict resolution, patterns of consumption and exchange, material culture, technology, infrastructure, gender relations, ethnicity, childrearing and socialization, religion, myth, symbols, values, etiquette, worldview, sports, music, nutrition, recreation, games, food, festivals, and language ( which is also the object of study in linguistic anthropology ).

An alphabet is a standard set of letters ( basic written symbols or graphemes ) which is used to write one or more languages based on the general principle that the letters represent phonemes ( basic significant sounds ) of the spoken language.

The vowels are significant in the Greek language, and the syllabical Linear B script which was used by the Mycenaean Greeks from the 16th century BC had 87 symbols including 5 vowels.

* A language may use different sets of symbols or different rules for distinct sets of vocabulary items, such as the Japanese hiragana and katakana syllabaries, or the various rules in English for spelling words from Latin and Greek, or the original Germanic vocabulary.

: Precise instructions ( in language understood by " the computer ") for a fast, efficient, " good " process that specifies the " moves " of " the computer " ( machine or human, equipped with the necessary internally contained information and capabilities ) to find, decode, and then process arbitrary input integers / symbols m and n, symbols + and =

Some of non verbal communication includes chronemics, haptics, gesture, body language or posture ; facial expression and eye contact, object communication such as clothing, hairstyles, architecture, symbols infographics, and tone of voice as well as through an aggregate of the above.

The first of these symbols were intended to be fully universal ; since Latin was the common language of science at that time, they were abbreviations based on the Latin names of metals – Cu comes from Cuprum, Fe comes from Ferrum, Ag from Argentum.

A formal grammar defines ( or generates ) a formal language, which is a ( usually infinite ) set of finite-length sequences of symbols ( i. e. strings ) that may be constructed by applying production rules to another sequence of symbols which initially contains just the start symbol.

Such a grammar defines the formal language: all words consisting solely of terminal symbols which can be reached by a derivation from the start symbol.

Transliteration systems are based on relating written symbols to one another, while transcription is the attempt to spell in one language the phonetic sounds of another.

Leontyev had seen human action as a result of biological as well as cultural evolution and, drawing on Marx's materialist conception of culture, stressed that individual cognition always is part of social action which in turn is mediated by man-made tools ( cultural artifacts ), language and other man-made systems of symbols, which he viewed as a major distinguishing feature of human culture and, thus, human cognition.

Oral language developed into written symbols and letters.

It is an assembly-style language for manipulating lists of symbols.

In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols.

The alphabet of a formal language is the set of symbols, letters, or tokens from which the strings of the language may be formed ; frequently it is required to be finite.

The terms and formulas of first-order logic are strings of symbols which together form the alphabet of the language.

Ubykh may be the language with the most fricatives ( 29 not including ), some of which do not have good symbols or diacritics in the IPA.

In typography and computing, the range of graphemes is broader than in a written language in other ways too: a typographical font often has to cope with a range of different languages each of which contribute their own graphemes, and it may also be required to print other symbols such as dingbats.

Their original alphabet was based on a spelling reform for English known as the Romic alphabet, but in order to make it usable for other languages, the values of the symbols were allowed to vary from language to language.