Chii nhamba mukuru? The Kudeuka uye zviduku nhamba

Kana munhu kudzidzira mumutende minwe zvakakwana kuona kuti vaviri nemapoka kufamba mubako, zviri zvishoma pane boka gomo. Asi paaingodzikisa paakaziva kuti yakadaro positional nhamba (nhamba rine nzvimbo chaiyo mumutsetse refu), akatanga kuti: chii rinotevera, chii nhamba mukuru?
Kubvira ipapo, yakanakisisa pfungwa akatanga kutsvaka, sei kuverenga tsika idzi, uye Chikurukuru, sei kuti kumuroora navo zvinoreva.

Dots pakupera akatevedzana

Kana vadzidzi nezvevanakomana yepakutanga pfungwa dzinongoitika nhamba, micheto nhamba nokuchenjera vakaisa Dots uye tsanangura kuti mukuru uye duku nhamba - a chikamu maturo. Zvinokwanisika nguva dzose kune kupfuura nhamba wedzera mumwe, uye haazovi pakukura. Asi mberi haana kunge zvichikwanisika kana kwaisava nokuda vaya vanoda kuwana zvinoreva munzvimbo hazvifaniri kuva.

Infinity nhamba dzakatevedzana, kuwedzera anotyisa uye Undefined tsika dzouzivi, akasika evasingatombonamati rwokugadzira matambudziko. Ndaifanira kutsvaka nan'anuro huru chaizvo nhamba. Pakutanga izvi zvakaitwa yoga nokuda mumapoka makuru mutauro, uye kukura kwenyika dzepasi pose akazviratidza mashoko, ndicho chikamu chikuru nhamba, zvakajairika munyika.

Gumi, zana, chiuru

mutauro ose nokuda nhamba hunobatsira kukosha, vakawana zita vayo.

In Russian zviri pakutanga nhamba kubva razero kusvika gumi. Up kumazana zvimwe nhamba dzinonzi uye yavo maererano, pamwe shoma Kuchinja midzi - "makumi" (vaviri gumi), "makumi" (zvitatu gumi), nezvimwewo, kana tiri zvinoumba "maviri-rimwe", "mashanu navana .. ". Kunze - pachinzvimbo "chetyredtsat" tine yamunenge, "mana."

The soro maviri-digit nhamba - "mapfumbamwe nemapfumbamwe" - remubatanidzwa zita. Uyezve, kubva mazita avo traditional - "zana" uye "chiuru", vamwe vari aumba kubva kurudyi mubatanidzwa. Ndizvo zvazvakaitawo nemamwe zvakafanana mitauro. Hazvina musoro kufunga kuti hwakagadzwa mazita vakapiwa kuwanda nenhamba, izvo nechokuita vakawanda vanhuwo zvavo. Kunyange ari chiuru nemombe aigona kupa akangofananawo murimi mudiki. With miriyoni imwe yakanga chakaoma, uye kuvhiringidzika akatanga.

Million, quintillion, detsilliard

In pakati XV remakore wokuFrance Nikolya Shuke kunan'anura nhamba kupfuura mukuru, zita racho chinorehwa nemashoko hurongwa pachishandiswa nevakariri sezviverengo pakati masayendisiti Latin. In Russian, havana kuchiita nadzurudzo nokuda nyore emashoko:

• 1 - Unus - Univ.
• 2 - navaviri, Bi (kaviri) - navaviri, bi.
• 3 - Tres - vatatu.
• 4 - Quattuor - Quadri.
• 5 - Quinque - zvikamu.
• 6 - Sex - Sexten.
• 7 - Septem - Sept.
• 8 - Octo - Octy.
• 9 - Novem - Noni.
• 10 - Decem - deci.

Hwaro mazita kwaiva kuva -illion, kubva "miriyoni" - "vanopfuura chiuru." -. Ie 1 000 000 - 1000 ^ 2 - zviuru pachivara. Shoko iri, kutaura guru nhamba, sezvaari akakurumbira seafarer Marco Polo uye musayendisiti. Saka, chiuru dhigirii yechitatu rava tiririyoni, 1000 ^ 4 - quadrillion. Imwe wokuFrance - Pelletier - akapa nokuda nhamba kuti vane Shyuke akadana "chimwe miriyoni chiuru" (10 ^ 9), "chiuru bhiriyoni" (10 ^ 15) uye zvichingodaro. e., shandisa kupedza "-illiard". Zvakazozivikanwa kuti bhiriyoni - ndicho bhiriyoni, 10 ^ 15 - Billiards, chikwata 21 razero - trilliard uye zvichingodaro.

Mazwi French mathematicians akatanga kushandiswa munyika dzakawanda. Asi zvishoma nezvishoma zvakava pachena kuti 10 ^ 9 Mune dzimwe zvinyorwa pakuzivikanwa kwete mabhiriyoni uye mabhiriyoni. Uye muUnited States vava hurongwa naro kuguma -illion wakaunganidza dhigirii pane miriyoni, kufanana French, asi zviuru. Somugumisiro, nhasi pane chikero mbiri munyika, "refu" uye "pfupi". Kuti tinzwisise kuti nhamba chinorehwa nezita Somuenzaniso, quadrillion, zviri nani kujekesa chii mwero nhamba akavaka 10. Kana rechi15 - ndiye "pfupi" pakafunuka vagamuchirwa neUnited States, Canada, muUK uye dzimwe nyika dzinoverengeka, kusanganisira Russia (kunyange hatina 10 ^ 9 bhiriyoni rimwe bhiriyoni), kana 24 - ndiye "refu", vakagamuchirwa munyika dzakawanda munyika.

Tredetsillion, vigintilliard uye milleillion

deci uye akaumba detsillion - - After rokupedzisira nhamba ndiyo Nhamba huru zvikuru kushandiswa pasina yakagozha shoko-idzodzo - 10 ^ 33 pfupi scale, nokuti zvinotevera mubatanidzwa akakodzera matomu anoshandiswa prefixes. Vakawana kunzwisisa remubatanidzwa mazita akafanana tredetsillion- 10 ^ 42, kvindetsillion - 10 ^ 48 uye saizvozvo unformulated, pachake mazita pakati VaRoma anokudzwa: .. Twenty - namakumi maviri, zana - uye chiuru ane zana - mille. Zvichitevera mitemo Shyuke anogona nokusingaperi kuumba mazita zvikara. Somuenzaniso, nhamba 10 ^ 308 760 anonzi dutsentduomilianongentnovemdetsillion.

Asi zvakagadzirwa aya anonakidza chete zvishoma nhamba yevanhu - hazvina kushandiswa tsika, uye tsika idzi pachavo havasi kusungwa kunyange yokungotaura matambudziko kana theorems. Zvakakunakirai kuti evasingatombonamati yokungotaura constructs ndiwo nhamba nemazihofori, dzimwe nguva kurapwa mazita sonorous chaizvo kana anotaurwa nezita romunyori.

Rima Legion asaṃkhyeya

Mubvunzo huru zviverengero akatambudzika uye "pre-kombiyuta" chizvarwa. The Slavs pane dzakawanda nhamba mugadziriro, vamwe havana kusvika pakakwirira mukuru; nhamba mukuru - 10 ^ 50. Mazita pauwandu kureba nguva yedu sokuti nhetembo, uye zvose kunyange vakanga hunobatsira zvahunoreva, rinozivikanwa chete dzekare uye nyanzvi dzemitauro: 10 ^ 4 - "rima", 10 ^ 5 - "Legion", 10 ^ 6 - "leodr" 10 ^ 7 - Vranje, namarudzi, 10 ^ 8 - "uriri."

No zvishoma yakanaka maererano rokuremekedza nhamba asaṃkhyeya anotaurwa mumagwaro wechiBuddha yekare Chinese uye yekare Indian muunganidzwa sutras. The quantitative Kukosha asaṃkhyeya Vanotsvakurudza zvakataurwa sezvo 10 ^ 140. Kuti unzwisise izvozvo zvakakwana naMwari pfungwa ndiro zvakadini yepasi pose zvinogara vanofanira kupfuura mweya kucheneswa panyama yose, akazviunganidzira pamusoro refu nzira kuberekwazve uye kuzowana yomufaro mukuru ine mamiriro Nirvana.

Googol, googolplex

A yemasvomhu pana Columbia University (USA) Edward Kasner kubva pakutanga 1920s vakatanga kufunga vazhinji. Zvikurukuru, iye aifarira sonorous uye kuratidza zita wakanaka nhamba 10 ^ 100. Rimwe zuva akanga achifamba pamwe vazukuru vake uye akavaudza pamusoro nhamba iyi. Nine gore Milton okuberekwa kunoburitsa Sirotta shoko googol - googol. Sekuru akasimuka kubva vazukuru uye bhonasi - nhamba itsva, zvavakanga akatsanangura sezvinotevera: chikwata uye zeros vakawanda unogona kunyora, asi kwete vose vakaneta. Name nhamba iyi yakanga googolplex. Pandinofungisisa, Kashner akasarudza kuti ichi chichava nhamba 10 ^ googol.

Zvinoreva nhamba dzakadaro Kashner ndaona zvakawanda kudzidzisa: sayenzi asingazivi chinhu chakadaro mari kuti mathematicians ramangwana pamuenzaniso wavo, akatsanangura kuti nhamba chikuru anogona kuchengeta kusiyana kusaverengeka.

Smart Pfungwa zita vaduku geniuses vaikoshesa havaoni ari boka kusimudzira itsva search engine. googol inotongwa paaimhanyisana uye waiva tsamba iwe, asi paiva zita, nokuti iro uwandu ephemeral anogona dzokuva chaiye - sezvo migove zhinji kuchava zvakakodzera.

Shannon nhamba, nhamba Schiusa, medzon, megiston

Kusiyana yefizikisi, nguva nenguva achimhanya mhiri zvokukwegura zvavakatemerwa pachisikigo, mathematicians mberi nzira pahunogumira. Munhu anoda nyama yemhuka wechesi Klod Shennon (1916-2001) vakazadzwa pfungwa nhamba 10 ^ 118 - zvikuru mikana zvinzvimbo vanogona kuitika mukati 40 unotii.

Stanley Schiusa kubva South Africa akanga achiparidza mumwe mabasa nomwe kuiswawo pakati pemazita ari "Millennium Challenge" - Riemann pfungwa. Iye anouya nokuwana mapatani ari kuparadzirwa inonyanya nhamba. Nokufamba pfungwa akashandisa yokutanga 10 ^ 10 ^ 10 ^ 34, akaratidza kuti SK ₁ achiteverwa 10 ^ 10 ^ 10 ^ 963 - rwechipiri nhamba Schiusa - SK _2.

Kushandisa nhamba idzi kunyange aenderane zvatinosiita yakarekodwa hurongwa. Gugo Shteyngauz (1887-1972) zvinganaka kushandisa geometric zvitarisiko: n mune netriangle - nayo N kune simba N, N akaenzana - N ari N zvokuridza, N mudenderedzwa - mumwe N iri N dzinoungana. Akatsanangura kuti hurongwa muenzaniso nhamba Mega - 2 mudenderedzwa, medzon - 3 mudenderedzwa, megiston - 10 ari denderedzwa. Saka zvakaoma kuziva Somuenzaniso, chikuru maviri digit nhamba, asi ishande rakakura zvakawanda akaita nyore.

Professor Donald Knuth zvairatidza museve notation, apo va- erection simba yakaratidzwa nomuseve, iyo inotorwa muitiro programmers. Googol iyi nyaya anotarira akafanana 10 ↑ 10 ↑ 2 uye googolplex - 10 ↑ 10 ↑ 10 ↑ 2.

nhamba Graham raMwari

Ronald Graham (P ra1935.), American yemasvomhu, vari kudzidza Ramsey dzidziso chokuita hypercubes - Multi-dimensional geometric mitumbi - kunge akatanga chaiyo nhamba G ₁ - G ₆₄ umo iye akataura chisarudzo muganhu, apo yokumusoro muganhu waiva kupfuura vakawanda ari nhamba, vaigamuchira zita rake. Iye kunyange afunga ekupedzisira 20 nhamba, uye kutanga Data vaiva zvinotevera tsika:

- G ₁ = 3 ↑↑↑↑ 3 = 8,7 x 10 ^ 115.

- G = ₂ 3 ↑ ... ↑ 3 (miseve kupfuura chero nhamba = G _1).

- G ₃ = 3 ↑ ... ↑ 3 (nhamba = G ₂ nokukurumidza kupfuura miseve).

...

- G = ₆₄ 3 ↑ ... ↑ 3 (nokukurumidza kupfuura nhamba chemiseve ₆₃ = G)

G _64, G rinomiririra chete, uye inyika guru kushandiswa kwemasvomhu kukarukureta nhamba. Zvakanyorwa mubhuku zvinyorwa. Submit kuti pakafunuka zvisingaiti, vakapiwa kuti vhoriyamu yose zvakasikwa anozivikanwa murume kwakunoitwa zviduku chairema bhuku (a kuutio neminondo ari Planck urefu (10 ^-35 m)), runoratidzwa nhamba 10 ^ 185.