Copyright © Philip M. Parker, INSEAD. Terms of Use.

Large Number

Definition: Large Number

Large Number

Noun

1. A large indefinite number; "a battalion of ants"; "a multitude of TV antennas".

Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved.
 


Synonyms: Large Number

Synonyms: battalion (n), multitude (n), pack (n). (additional references)

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Specialty Definition: Large number

(From Wikipedia, the free Encyclopedia)

Large numbers are numbers that are large compared with the numbers used in everyday life. Very large numbers often occur in fields such as mathematics, cosmology and cryptography. Sometimes people refer to numbers as being "astronomically large".

Large numbers in the everyday world

Large numbers are often found in science, and scientific notation was created to handle both these large numbers and also very small numbers. Some large numbers apply to things in the everyday world.

Examples of large numbers describing everyday real-world objects are:

Other large numbers are found in astronomy: Large numbers are found in fields such as mathematics and cryptography.

The MD5 hash function generates 128-bit results. There are thus 2128 (approximately 3.402×1038) possible MD5 hash values. If the MD5 function is a good hash function, the chance of a document having a particular hash value is 2-128, a value that can be regarded as equivalent to zero for most practical purposes. (But see birthday paradox.)

However, this is still a small number compared with the estimated number of atoms in the Earth, still less compared with the estimated number of atoms in the observable universe.

Even larger numbers

Combinatorial processes rapidly generate even larger numbers. The factorial function, which defines the number of permutations of a set of unique objects, grows very rapidly with the number of objects.

Combinatorial processes generate very large numbers in statistical mechanics. These numbers are so large that they are typically only referred to using their logarithms.

Gödel numbers, and similar numbers used to represent bit-strings in algorithmic information theory are very large, even for mathematical statements of reasonable length. However, some pathological numbers are even larger than the Gödel numbers of typical mathematical propositions.

Uncomputably large numbers

The busy beaver function Σ is an example of a function which grows faster than any computable function. Consequently, its value for even relatively small input is huge. The values of Σ(n) for n = 1, 2, 3, 4 are 1, 4, 6, 13. Σ(5) is not known but is definitely ≥ 4098. Σ(6) is at least 1.29×10865.

To infinity, and beyond

Although all these numbers above are very large, they are all still finite. Some fields of mathematics define infinite and transfinite numbers.

Beyond all these, Georg Cantor's conception of the Absolute Infinite surely represents the absolute largest possible concept of "large number".

Notations

Many mathematicians have devised special notations to denote exactly how big a "large number" really is.

The Knuth arrow is a very simple notation that describes power towers. For larger power towers, it is preferrable to use hyper notation.

Steinhaus polygon notation and Moser polygon notation extend the idea further and use polygons to show this idea.

See also

External links

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Large number."

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Synonyms within Context: Large Number

ContextSynonyms within Context (source: adapted from Roget's Thesaurus).

Multitude

Noun: multitude; numerous; Adjective: numerosity, numerality; multiplicity; profusion; (plenty); legion, host; great number, large number, round number, enormous number; a quantity, numbers, array, sight, army, sea, galaxy; scores, peck, bushel, shoal, swarm, draught, bevy, cloud, flock, herd, drove, flight, covey, hive, brood, litter, farrow, fry, nest; crowd; (assemblage); lots; all in the world and his wife.

Source: adapted from Roget's Thesaurus.

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Crosswords: Large Number

English words defined with "large number": A block of shares, army, AscococcusBantu, batch, Bernoulli's law, bigCISC, complex instruction set computer, complex instruction set computing, crowddeal, dozens, Drusedeconomies of scale, Epidemical, Equal decrement of lifeflockgobs, good deal, great dealhatful, heap, heapsinvolvedjoint-stock companylarge, lashings, Law of error, Law of frequency of error, law of large numbers, Law of mortality, Lernaeacea, loads, Locomotive boiler, Longicornia, lot, lotsmany a, mass, massacre, mess, mickle, mint, Moving day, mow down, muckle, multiplicity, multitudinousness, Myohaematinnumber cruncher, numerosity, numerousness, Nummulitesoodlespeck, Pentamethylene, Phyllopoda, pile, piles, plenty, pot, Pyrrolquite a littleraft, rafts, Rhipidoglossascads, scores, sight, Siphonostomata, slaughter, slew, slews, spate, spinning jenny, stack, stacksTaenioglossa, Thiophene, tidy sum, tonswad, wads, whole lot, whole slewZoocyst. (references)
Specialty definitions using "large number": advanced fleet anchorage, Antigens, CD13, avalanche effectBevoriskius, bit stuffingCarbohydrate-Deficient Glycoprotein Syndrome, Catiline's Conspiracy, Chlordecone, coal mining methods, code division multiple access, code-division multiple access, commercial sampling of coal, considered harmful, cooperative groupDevil and Dr. Faustus, Digital Subscriber Line, DNA computingequation of stateGas Centrifuge, geochemical mapping, Gullstrand's schematic eyehigh rise, Hopkinson chain machine, hypervascularintermittency effectJoint Academic NETworkkremvaxlarge-scale integration, Linux, LSImarket risk, mass shooting, massively parallel computer, massively parallel processor, memetic algorithm, mining disaster, Mongolian Hordes technique, multiplexorNewaygo screenparallel distributed processing, peripheral polyneuropathy, peripheral pump, Poisson distributions, Polycystic Kidney Diseases, Powerful sight, p-typeQuite a fewReceptors, Odorant, regenerative pump, retro-reflecting material, RISC OSsawtooth stoping, schematic eye, shield basalt, Sight, Solitary Nucleus, station having light traffic, steel tendon, Summary File, SuperJanet, systematic riskTownsend avalanche, Townsend ionisation, Townsend ionization, type B distributionundiversifiable riskVertical coordination, voluntary chainsWide SCSIZinc Fingers. (references)

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Photo Album: Large Number

ThumbnailDescription & CreditThumbnailDescription & Credit

This is a histological slide stained with H&E of a human herpesvirus (HHV-6), a type of human herpes virus. In this photomicrograph of infected cells, the black specks indicate the location of a radioactive isotope that has been attached to the viral RNA. In this case, a large number of black specks indicate that this lymphocyte has been infected. Credit: Unknown photographer/artist.

STAN, short for "standard man," is able to talk, breathe, blink its eyes, and mimic a large number of other human actions. By displaying any number of "casualty symptoms," STAN will provide valuable training for Air Force nurses as par.

In Lockwood's Basin, Boston, Massachusetts, in 1918. Also present are a large number of section patrol boats. Photographed by Alton M. Blackinton, Boston. Credit: NAVY.

Underway at sea, 1954. Note large number of boats stowed on board. Credit: NAVY.

USS Lexington (CV-2) during the action, seen from USS Yorktown (CV-5), 8 May 1942. Large number of planes on deck and low sun indicate that the photo was taken early in the morning, prior to launching the strike against the Japanese carrier force. Yorktown has several SBDs and F4Fs on deck with engines running, apparently preparing to take off. Lexington, whose silhouette has been altered by the earlier removal of her 8-inch gun turrets, has planes parked fore and aft, and may be respotting her deck in preparation for launching aircraft. Credit: NAVY.

Line engraving published in "Harper's Weekly", July-December 1861, pages 456-457, depicting a large number of Navy ships off the New York Navy Yard, early in the Civil War. Vessels shown include (from left to right): USS Montgomery; USS Vandalia; USSBrandywine; USS North Carolina; USS Potomac; USS Savannah; USS R.R. Cuyler; USS Mount Vernon; USS Roanoke; USS Resolute and USS Wabash. A rowing launch is underway in the foreground. Credit: NAVY.

Pleasant View--showing large number of guests in front of house / Kimball, photo. Credit: Library of Congress.

Branch meeting of large number of NAACP executives, Washington, D.C. Credit: Library of Congress.

Steel, bronze, and aluminum gear blanks. A Brooklyn manufacturer holding marine contracts is seeking subcontractng facilities for the production of a large number of gear blanks of various sizes and shapes. Credit: Library of Congress.

Entrance to rooming house and lodge hall, Silverton, Colorado. There are always many rooming and boarding houses in mining towns to accomodate the large number of single men working in the mines and mills. Credit: Library of Congress.

Source: pictures compiled by the editor from various references; see picture credits.

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Historic Usage: Large Number

AuthorDateQuotation

Winston S. Churchill

1946

Already we use together a large number of islands; more may well be entrusted to our joint care in the near future. ("Iron Curtain" Speech)

Source: compiled by the editor from various references.

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Use in Literature: Large Number

TitleAuthorQuote

Les Miserables

Hugo, Victor

A very large number of streets, now vaulted, were then hollow causeways.

Source: compiled by the editor from various references.

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Non-Fiction Usage: Large Number

SubjectTopicQuote

Health

Nonetheless, a large number of people get into serious trouble because of their drinking. (references)

It fails a relatively large number of babies whose hearing sensitivity is, in fact, normal. (references)

Nevertheless, a large number of the listed Web sites provide useful background information. (references)

Business

This refers to a very large number of consumer and other goods, including cosmetic products. (references)

AutoCAD is the most popular environment, used by a large number of Autodesk's partners to write their own applications. (references)

The local firms may or may not have any foreign employees, while the foreign firms employ a large number of local staff. (references)

Children

Burma

Because of landmine detonations, there are a large number of amputees. (references)

Saint Vincent and the Grenadines

One underlying cause is the large number of children born to teenage mothers. (references)

Kyrgyz Republic

A range of serious nutrition-related problems affected a large number of children, especially in rural areas. (references)

Civil Liberties

Chad

In May 2000, the Sultan of Kanem arrested a large number of Fayda al-Jahria adherents. (references)

Thailand

However, NGO's reported that a large number of those deported later returned to the country. (references)

Kyrgyz Republic

The rally concluded peacefully without interference from the large number of uniformed and plainclothes militia present. (references)

Economic History

Sri Lanka

Further, a large number of tender board officials have been trained. (references)

Ukraine

A striking feature of the market is the large number of MC operators. (references)

Netherlands

A large number (over 220) of small and medium sized suppliers characterizes the industry. (references)

Human Rights

Botswana

Pretrial detention has been prolonged in a large number of cases. (references)

Algeria

In addition the Government detained a large number of persons for short periods in connection with the violence. (references)

Solomon Islands

Slow adjudication of the large number of cases before the courts has resulted in long delays before cases go to trial. (references)

Minorities

Germany

All branches of Islam are represented in the country, with the vast majority of Muslims coming from a large number of other countries. (references)

Political Economy

Sudan

The Government allowed a large number of refugees to work. (references)

Romania

There was a large number of impoverished homeless children in large cities. (references)

Political Rights

Zimbabwe

The voters' roll has been computerized, but it contains a large number of redundancies and errors, including misspellings, multiple entries, and names of deceased persons. (references)

Mozambique

Due to a large number of illiterate voters, there were a significant number of ballots on which preferences were unclear and which required interpretation by the National Electoral Commission. (references)

Tajikistan

Most observers and citizens believed that the large number of appointed and indirectly elected members of the upper house made the elections largely pointless and it was assumed that these elections would result in the distribution of political favors by the ruling party. (references)

Trade

Indonesia

Prior to the financial crisis, a large number of Indonesian banks maintained correspondent relationships with American banks. (references)

Nepal

Both banks reportedly have a large number of non-performing loans which, if written to market, would make the banks technically insolvent. (references)

Korea

Korea's average basic tariff in 2000 is about 7.9%. Duties still remain very high on a large number of high-value agricultural and fisheries products. (references)

Travel

Taiwan

Accommodations and Housing: Taiwan has a large number of international- and domestic-standard hotels, hostels and inns. (references)

Cote D'ivoire

There are a large number of "polycliniques" in Abidjan, the largest and probably best being the Polyclinique Internationale de Sainte Anne Marie (PISAM). (references)

Ireland

In view of the large number of visitors going to Ireland, business travelers are advised to make their hotel reservations well in advance, especially during the summer months, in order to assure the needed accommodations. (references)

Women

Cameroon

While there are no reliable statistics on violence against women, the large number of newspaper reports, which observers believe are a fraction of actual incidents, indicated that it is widespread. (references)

Brazil

For example, in the state of Sao Paulo, there were 310,058 complaints of violence against women in 2000, compared with 263,702 in 1999. This included 2,403 reported cases of rape or attempted rape in 2000, compared with 2,386 for 1999. In the Federal District, the number of reported cases of rape declined slightly to 371 during 2000, compared with 416 cases in 1999. The annual number of cases of harmful physical assault against women reported to the police in the state of Rio de Janeiro nearly doubled from 1991 to 1999, to 34,831, and the number of rapes reported increased from 952 to 1,455. Both state authorities and women's rights activists agree that a large number of rapes go unreported. (references)

Worker Rights

Thailand

The majority of prostitutes are not kept under physical constraint, but a large number work in debt bondage. (references)

Source: compiled by the editor from ICON Group International, Inc.; see credits.

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Speeches: Large Number

SpeakerTermPhrase(s)

Benjamin Harrison

1889-1893The civil list is so large that a personal knowledge of any large number of the applicants is impossible.

Harry S. Truman

1945-1953In fact, if any large number of workers earn less than this amount, we will find it impossible to maintain the levels of purchasing power needed to sustain the stable prosperity which we desire.

Bill Clinton

1993-2001Today there are large number of vacancies in the federal courts.

Source: compiled by the editor from various references.

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Expressions: Large Number

Expressions using "large number": a large number of large number of. Additional references.

Source: compiled by the editor from various references; see credits.

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Modern Translation: Large Number

Language Translations for "large number"; alternative meanings/domain in parentheses.

Chinese 

  

千軍萬馬 (a strong army with thousands of horses; large number of people). (various references)

   

Danish

  

smaa parti af et stort antal varianter (small batch of a large number of variants), polyneuritis (polyneuritis), perifer polyneuropati (marked by paralysis, pain and wasting of muscles may be caused by exposure to organic solvents or lead, peripheral polyneuropathy, polyneuritis, simultaneous inflammation of a large number of the spinal nerves), man kan let forestille sig,at kontakten mellem metalstraalen og den kolde kokillevaeg i kombination med den kraftige omroering ved udstoebningen,kunne give anledning til dannelse af et stort antal krystaller,af hvilke et stort antal kunne give en lagforme (combined with the vigorous currents produced during teeming, in fact, of which some would form a thin skin zone adhering to the walls but of which others would remain in suspension in the liquid, one can, readily imagine that the contact between the stream of liquid metal and the cold mould, would give rise to a large number of crystallites). (various references)

   

Dutch

  

polyneuropathie (marked by paralysis, pain and wasting of muscles may be caused by exposure to organic solvents or lead, peripheral polyneuropathy, polyneuritis, simultaneous inflammation of a large number of the spinal nerves), polyneuritis (polyneuritis), men kan zich werkelijk voorstellen dat tengevolge van het contact tussen de stroom van vloeibaar metaal en de koude gietvorm,te zamen met de heftige stromingen die tijdens het gieten optreden,een groot aantal kristallieten ontstaan waarvan een deel een du (combined with the vigorous currents produced during teeming, in fact, of which some would form a thin skin zone adhering to the walls but of which others would remain in suspension in the liquid, one can, readily imagine that the contact between the stream of liquid metal and the cold mould, would give rise to a large number of crystallites), kleine serie met veel varianten (small batch of a large number of variants). (various references)

   

Finnish

  

väsymislujuus (a large number of load cycles for determining the fatigue strength, endurance limit, fatigue strength at N cycles, fatigue strength for finite life), suuri määrä (a large number), polyneuriitti (marked by paralysis, pain and wasting of muscles may be caused by exposure to organic solvents or lead, peripheral polyneuropathy, polyneuritis, simultaneous inflammation of a large number of the spinal nerves), jännitysjaksojen lukumäärä (a large number of load cycles for determining the fatigue strength). (various references)

   

French

  

grande quantité. (various references)

   

German

  

Polyneuritis (polyneuritis), man kann sich wirklich vorstellen, dass der die kalte Kokille beruehrende Giesstrahl und die heftigen Stroemungen, die waehrend des Giessens auftreten, eine grosse Anzahl von Kristalliten ergeben, von denen manche eine schichtfoermige, an die Waende angeh (combined with the vigorous currents produced during teeming, in fact, of which some would form a thin skin zone adhering to the walls but of which others would remain in suspension in the liquid, one can, readily imagine that the contact between the stream of liquid metal and the cold mould, would give rise to a large number of crystallites), kleine Stückzahl zahlreicher Varianten (small batch of a large number of variants), hohe Lastspielzahlen fuer den Bereich der Dauerfestigkeit (a large number of load cycles for determining the fatigue strength). (various references)

   

Greek 

  

μικρή παρτίδα προϊόντων με μεγάλο αριθμό παραλλαγών (small batch of a large number of variants), μπορούμε πράγματι να υποθέσουμε οτι η επαφή με το ψυχρό πλίνθωμα συνδυασμένη με τα βίαια ρεύματα τα οποία δημιουργούνται κατά την χύτευση, (would give rise to a large number of crystallites), μεγάλος αριθμός κύκλων φορτίου για τον προσδιορισμό της αντοχής σε κόπωση (a large number of load cycles for determining the fatigue strength), πλήθοσ (a lot of, army, battalion, bevy, crowd, heaps, host, huddle, large number of, lots, multitude, plenty of, ruck, shoal, swarm, throng, troop), πολυνευρίτιδα (bulbar neuritis, marked by paralysis, pain and wasting of muscles may be caused by exposure to organic solvents or lead, peripheral polyneuropathy, polyneuritis, simultaneous inflammation of a large number of the spinal nerves). (various references)

   

Hungarian

  

som ember (a large number of men, large number of men), sok férfi (a large number of men, large number of men). (various references)

   

Italian

  

polineuropatia periferica (marked by paralysis, pain and wasting of muscles may be caused by exposure to organic solvents or lead, peripheral polyneuropathy, polyneuritis, simultaneous inflammation of a large number of the spinal nerves), polineurite (polyneuritis), piccolo lotto di una vasta gamma di varianti (small batch of a large number of variants), Ci si puo di fatto figurare che il getto di colata che viene a contatto con la lingottiera fredda e le forti correnti che si formano nella colata generino una grande quantit di cristalliti, delle quali alcune formano una zona stratificata aderente alle (combined with the vigorous currents produced during teeming, in fact, of which some would form a thin skin zone adhering to the walls but of which others would remain in suspension in the liquid, one can, readily imagine that the contact between the stream of liquid metal and the cold mould, would give rise to a large number of crystallites), alto numero di cicli per determinare il limite di fatica (a large number of load cycles for determining the fatigue strength). (various references)

   

Japanese Kanji 

  

百鬼夜行 (a large number of people plotting and doing evil, a scandalous scene, a veritable pandemonium), 群臣 (a crowd or large number of one's retainers or subjects), 多人数 (large number of people), 不特定多数 (unspecified large number). (various references)

   

Japanese Katakana 

  

たに"ずう (large number of people), たに"ず (large number of people), ぐ"し" (a crowd or large number of one's retainers or subjects, god of war, war hero), ひゃっきやぎょう (a large number of people plotting and doing evil, a scandalous scene, a veritable pandemonium), ひゃっきや"う (a large number of people plotting and doing evil, a scandalous scene, a veritable pandemonium), ふとくていたすう (unspecified large number). (various references)

   

Manx

  

lansh (a great deal, a large quantity, a lot), lab (a lot). (various references)

   

Pig Latin

  

argelay umbernay

   

Portuguese

  

polinevrite (polyneuritis), polineuropatia periférica (marked by paralysis, pain and wasting of muscles may be caused by exposure to organic solvents or lead, peripheral polyneuropathy, polyneuritis, simultaneous inflammation of a large number of the spinal nerves), pode-se com efeito pensar que,o contacto com a lingoteira fria do jacto e das correntes violentas produzidas durante o vazamento,dá lugar a um grande número de cristalites,das quais algumas formam como que uma "pele" aderente s paredes,enquanto outras, pequeno lote de um grande número de variantes (small batch of a large number of variants). (various references)

   

Russian 

  

большой число. (various references)

   

Spanish

  

un número elevado de ciclos de carga para determinar la resistencia a la fatiga (a large number of load cycles for determining the fatigue strength), pequeño lote de gran número de variantes (small batch of a large number of variants), en realidad, se puede pensar que el contacto con la lingotera fría del chorro y de las corrientes violentas producidas durante la colada dan gran número de cristales de los cuales algunos producen una zona pelicular adherente a las paredes, mientras que (combined with the vigorous currents produced during teeming, in fact, of which some would form a thin skin zone adhering to the walls but of which others would remain in suspension in the liquid, one can, readily imagine that the contact between the stream of liquid metal and the cold mould, would give rise to a large number of crystallites). (various references)

   

Swedish

  

ganska mycket (a good deal, a large number of, fair amount, very much). (various references)

Source: compiled by the editor from various translation references.

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Anagrams: Large Number

Scrabble® Enable2K-Verified Anagrams

Words within the letters "a-b-e-e-g-l-m-n-r-r-u"

-2 letters: embrangle, numerable.

-3 letters: bargemen, enlarger, grumbler, lumberer, numberer, renumber.

-4 letters: albumen, auberge, blunger, bungler, burglar, enabler, enlarge, euglena, gambler, gambrel, garbler, general, gerbera, germane, gleamer, gleaner, gleeman, granule, grueler, grumble, leaguer, learner, mangler, manurer, marbler, melange, nebulae, nebular, numeral, rambler, reargue, rebegan, rebegun, regaler, regular, relearn, rumbler, umbrage, uneager, urbaner.

-5 letters: almner, ambeer, ambler.

Source: compiled by the editor from various references; see credits.

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INDEX

1. Definition
2. Synonyms
3. Crosswords
4. Images: Photo Album
5. Quotations: Historic
6. Quotations: Fiction
7. Quotations: Non-fiction
8. Quotations: Speeches
9. Expressions
10. Translations: Modern
11. Anagrams
12. Bibliography


  

Copyright © Philip M. Parker, INSEAD. Terms of Use.