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17-letter words containing a, r, e, n, o, t

  • national security — defence of a country
  • natural deduction — (logic)   A set of rules expressing how valid proofs may be constructed in predicate logic. In the traditional notation, a horizontal line separates premises (above) from conclusions (below). Vertical ellipsis (dots) stand for a series of applications of the rules. "T" is the constant "true" and "F" is the constant "false" (sometimes written with a LaTeX \perp). "^" is the AND (conjunction) operator, "v" is the inclusive OR (disjunction) operator and "/" is NOT (negation or complement, normally written with a LaTeX \neg). P, Q, P1, P2, etc. stand for propositions such as "Socrates was a man". P[x] is a proposition possibly containing instances of the variable x, e.g. "x can fly". A proof (a sequence of applications of the rules) may be enclosed in a box. A boxed proof produces conclusions that are only valid given the assumptions made inside the box, however, the proof demonstrates certain relationships which are valid outside the box. For example, the box below labelled "Implication introduction" starts by assuming P, which need not be a true proposition so long as it can be used to derive Q. Truth introduction: - T (Truth is free). Binary AND introduction: ----------- | . | . | | . | . | | Q1 | Q2 | ----------- Q1 ^ Q2 (If we can derive both Q1 and Q2 then Q1^Q2 is true). N-ary AND introduction: ---------------- | . | .. | . | | . | .. | . | | Q1 | .. | Qn | ---------------- Q1^..^Qi^..^Qn Other n-ary rules follow the binary versions similarly. Quantified AND introduction: --------- | x . | | . | | Q[x] | --------- For all x . Q[x] (If we can prove Q for arbitrary x then Q is true for all x). Falsity elimination: F - Q (Falsity opens the floodgates). OR elimination: P1 v P2 ----------- | P1 | P2 | | . | . | | . | . | | Q | Q | ----------- Q (Given P1 v P2, if Q follows from both then Q is true). Exists elimination: Exists x . P[x] ----------- | x P[x] | | . | | . | | Q | ----------- Q (If Q follows from P[x] for arbitrary x and such an x exists then Q is true). OR introduction 1: P1 ------- P1 v P2 (If P1 is true then P1 OR anything is true). OR introduction 2: P2 ------- P1 v P2 (If P2 is true then anything OR P2 is true). Similar symmetries apply to ^ rules. Exists introduction: P[a] ------------- Exists x.P[x] (If P is true for "a" then it is true for all x). AND elimination 1: P1 ^ P2 ------- P1 (If P1 and P2 are true then P1 is true). For all elimination: For all x . P[x] ---------------- P[a] (If P is true for all x then it is true for "a"). For all implication introduction: ----------- | x P[x] | | . | | . | | Q[x] | ----------- For all x . P[x] -> Q[x] (If Q follows from P for arbitrary x then Q follows from P for all x). Implication introduction: ----- | P | | . | | . | | Q | ----- P -> Q (If Q follows from P then P implies Q). NOT introduction: ----- | P | | . | | . | | F | ----- / P (If falsity follows from P then P is false). NOT-NOT: //P --- P (If it is not the case that P is not true then P is true). For all implies exists: P[a] For all x . P[x] -> Q[x] ------------------------------- Q[a] (If P is true for given "a" and P implies Q for all x then Q is true for a). Implication elimination, modus ponens: P P -> Q ---------- Q (If P and P implies Q then Q). NOT elimination, contradiction: P /P ------ F (If P is true and P is not true then false is true).
  • natural resources — a naturally occurring source of wealth, as land or water.
  • natural selection — the process by which forms of life having traits that better enable them to adapt to specific environmental pressures, as predators, changes in climate, or competition for food or mates, will tend to survive and reproduce in greater numbers than others of their kind, thus ensuring the perpetuation of those favorable traits in succeeding generations.
  • natural-resources — a naturally occurring source of wealth, as land or water.
  • naval observatory — an astronomical observatory located in Washington, D.C., operated by the U.S. government, and responsible for the U.S. time service.
  • near-earth object — a comet or asteroid pushed by the gravitational attraction of nearby planets into an orbit that allows it to enter the earth's orbit and thereby pose a danger of collision. Abbreviation: NEO.
  • neath port talbot — a county borough in S Wales, created from part of West Glamorgan in 1996. Administrative centre: Port Talbot. Pop: 135 300 (2003 est). Area: 439 sq km (169 sq miles)
  • negative polarity — the grammatical character of a word or phrase, such as ever or any, that may normally be used only in a semantically or syntactically negative or interrogative context
  • nephelometrically — By means of nephelometry.
  • network marketing — a marketing strategy in which sales representatives of a company recruit other salespeople and earn commissions on their own sales and on the sales made by their team: Use your personal relationships to be successful in network marketing.
  • neurodegenerative — Resulting in or characterized by degeneration of the nervous system, especially the neurons in the brain.
  • neurofibromatosis — a dominantly inherited genetic disorder characterized by flat brown patches on the skin, neurofibromas of the skin and internal organs, and in some cases skeletal deformity.
  • neuropathological — (medicine) Of, pertaining to, or arising from neuropathology, the pathology of nerve tissue.
  • neuropsychiatrist — A medical doctor specializing in neuropsychiatry; a medical doctor dealing with disorders that have both neurological and psychiatric features.
  • neurotransmission — the transmission of a nerve impulse across a synapse.
  • neurotransmissive — Relating to neurotransmission.
  • neurotransmitters — Plural form of neurotransmitter.
  • new orleans style — a style of jazz developed in New Orleans early in the 20th century, influenced by blues, ragtime, marching band music, and minstrelsy and marked by polyphonic group improvisation.
  • new scotland yard — See under Scotland Yard (def 1).
  • ninety-day wonder — an officer commissioned in a branch of the armed forces after an unusually short training period, especially after a three-months officers' training course during World War II.
  • nitrogen fixation — any process of combining atmospheric nitrogen with other elements, either by chemical means or by bacterial action: used chiefly in the preparation of fertilizers, industrial products, etc.
  • nitrogen narcosis — a semistupor, lightheadedness, or euphoria experienced by deep-sea divers when nitrogen from air enters the blood at higher than atmospheric pressure.
  • non-argumentative — fond of or given to argument and dispute; disputatious; contentious: The law students were an unusually argumentative group.
  • non-authoritative — having due authority; having the sanction or weight of authority: an authoritative opinion.
  • non-certification — the act of certifying.
  • non-consideration — the act of considering; careful thought; meditation; deliberation: I will give your project full consideration.
  • non-containerized — to package (freight) in uniform, sealed containers for shipment.
  • non-controversial — of, relating to, or characteristic of controversy, or prolonged public dispute, debate, or contention; polemical: a controversial book.
  • non-demonstrative — characterized by or given to open exhibition or expression of one's emotions, attitudes, etc., especially of love or affection: She wished her fiancé were more demonstrative.
  • non-discretionary — subject or left to one's own discretion.
  • non-environmental — the aggregate of surrounding things, conditions, or influences; surroundings; milieu.
  • non-materialistic — excessively concerned with physical comforts or the acquisition of wealth and material possessions, rather than with spiritual, intellectual, or cultural values.
  • non-proliferation — Non-proliferation is the limiting of the production and spread of something such as nuclear or chemical weapons.
  • non-reciprocating — to give, feel, etc., in return.
  • non-retroactivity — operative with respect to past occurrences, as a statute; retrospective: a retroactive law.
  • non-stereotypical — a process, now often replaced by more advanced methods, for making metal printing plates by taking a mold of composed type or the like in papier-mâché or other material and then taking from this mold a cast in type metal.
  • non-thermoplastic — soft and pliable when heated, as some plastics, without any change of the inherent properties.
  • nonimpact printer — a printer that creates images without mechanically impacting the page, as an ink-jet or laser printer.
  • noninertial frame — a frame of reference that moves with the object, so that the moving object appears to violate Newton's laws of motion since it accelerates despite having no horizontal forces on it.
  • nonrepresentative — a person or thing that represents another or others.
  • nonunderstandable — Not understandable.
  • nord-ostsee kanal — German name of Kiel Canal.
  • north lanarkshire — a council area of central Scotland: consists mainly of the NE part of the historical county of Lanarkshire; formerly (1974–96) part of Strathclyde Region: engineering and metalworking industries. Administrative centre: Motherwell. Pop: 321 820 (2003 est). Area: 1771 sq km (684 sq miles)
  • north miami beach — a city in SE Florida.
  • north-wall hammer — a type of ice axe that has a hammer as part of its head
  • northeast by east — a point on the compass 11°15′ east of northeast. Abbreviation: NEbE.
  • northeast passage — a ship route along the N coast of Europe and Asia, between the North Sea and the Pacific.
  • northern michigan — the peninsula between lakes Superior and Michigan constituting the N part of Michigan. Abbreviation: U.P.
  • northern rhodesia — former name of Zambia.
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