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# completeness axiom

аксиома полноты

Большой англо-русский и русско-английский словарь. 2001.

### Смотреть что такое "completeness axiom" в других словарях:

• Completeness axiom — In mathematics the completeness axiom, also called Dedekind completeness of the real numbers, is a fundamental property of the set R of real numbers. It is the property that distinguishes R from other ordered fields, especially from the set of… …   Wikipedia

• completeness axiom — noun The following axiom (applied to an ordered field): for any subset of the given ordered field, if there is any upper bound for this subset, then there is also a supremum for this subset, and this supremum is an element of the given ordered… …   Wiktionary

• Completeness of the real numbers — Intuitively, completeness implies that there are not any “gaps” (in Dedekind s terminology) or “missing points” in the real number line. This contrasts with the rational numbers, whose corresponding number line has a “gap” at each irrational… …   Wikipedia

• Axiom of Archimedes — The axiom of Archimedes can be stated in modern notation as follows: Let x be any real number. Then there exists a natural number n such that n > x. In field theory this statement is called the Axiom of Archimedes. The same name is also applied… …   Wikipedia

• Axiom — This article is about logical propositions. For other uses, see Axiom (disambiguation). In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self evident or to define and… …   Wikipedia

• Completeness — In general, an object is complete if nothing needs to be added to it. This notion is made more specific in various fields. Contents 1 Logical completeness 2 Mathematical completeness 3 Computing 4 …   Wikipedia

• Axiom of choice — This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band). In mathematics, the axiom of choice, or AC, is an axiom of set theory stating that for every family of nonempty sets there exists a family of …   Wikipedia

• Completeness (order theory) — In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset). A special use of the term refers to complete partial orders or complete lattices.… …   Wikipedia

• Completeness — Vollständigkeit ist eine Eigenschaft formaler Systeme bzw. Kalküle. Man unterscheidet semantische Vollständigkeit („Alles, was wahr ist, ist beweisbar.“), klassische Vollständigkeit („Eine der zwei Aussagen und ist stets beweisbar.“) und… …   Deutsch Wikipedia

• completeness — Intuitively, a logical system is complete if everything that we want can be derived in it. Thus a formalization of logic is complete if all logically valid forms of argument are derivable in the system; a system designed to codify mathematical… …   Philosophy dictionary

• Gödel's completeness theorem — is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first order logic. It was first proved by Kurt Gödel in 1929. A first order formula is called logically valid if… …   Wikipedia

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