Imbali yenombolo zero. Yintoni inombolo 0?

Imfuneko ukubala kwabonakala kumntu ukususela ekuqaleni lokusekwa yoluntu kwakudala. iinkqubo zabo lwamanani, kunye amanani reference ethile, kwasekwa onke amaziko ezahlukeneyo impucuko eYiputa naseBhabhiloni yamandulo, China ne-Indiya, kunye South American amaNdiya Greece yamandulo. Mathematics iye yaphuhliswa ukusuka ukubala olula izinto ukusombulula esimbaxa theory yethopholoji efanayo. Kulo mzekelo, ibali zero abe iqhezu elincinane kuphela kweli thuba.

Amanani kunye nezibalo

Ukususela nullis Latin ( "no") lo gama enye yezi ngongoma zibalulekileyo zezibalo. Oku kuquka kuphela isimboli - isafobe enceda ukuba amanqaku, imisebenzi zezibalo irekhodi. Le mbono wonke. Ukungabikho nayiphi na imali, ubuze, isiqalo engenasiphelo - sengqondo yentanda ukuba la magama ayehlukile zaphawula ezahlukeneyo, kwiinkqubo ezahlukeneyo inqubo.

ngenkqubo yokubhala inani ngokokuma

Kumaxesha ukuhlinza, calculus uncedo ugcine iminwe neenzwane. amanani Yahlula kwi ngezihlanu kunye bamashumi, imvelaphi kwesishumi inkqubo inani ihlobene oku. Kwixa elizayo, ukuze kube lula le misebenzi, kule khosi kwakukho nicks phezu kweenkuni kunye nezilwanyana amathambo, serifs phezu amatye, iingqalutye. ekonookrwece nezinye izinto ezincinci. element nganye enjalo ibonisa inani elithile. akumila kunjeya imifuziselo asebenzisekayo ngamanani. iinkqubo ezinjalo kuthiwa ngokokuma - amanani ixabiso xa ubhala amanani emiselwe izikhundla zawo okanye ukuchithwa.

Umzekelo ndlela esahlukileyo, kwaye nangoku inkqubo esetyenziswayo yindlela lokubhala lifikile phantsi ukususela ngexesha eRoma yamandulo. Kuyo ukuba ityumbe iiyunithi, amashumi, amakhulu basebenzisa oonobumba be-alfabhethi Latin.

abacus

ibhodi Audit, eliquka kwemingxuma esihambelanayo kwiindawo ezithile, apho ibekwe iingqalutye okanye amaso, uyiqhelile ukuya iinkcubeko beentlanga ezahlukeneyo kunye eziqaphelekayo. Kukho ezinye iintlobo ngeentlobo Abaca - intambo kunye amaqhina okanye ngeentambo kunye amaso. Inqanaba elilandelayo kuphuhliso izixhobo ezinjalo amanqaku ezazisetyenziswa phambi kokufika zokubala.

History of inani zero - yinkqubo wesiseko iingqiqo zemathematika kunye ekuqaleni ukusetyenziswa iisimboli, ekhombisa. Kwaye ke abacus, kunye namanqaku, ngandlela ithile, yaye njengendlela nokuthelekelela lwe thotho wokwamanani. kwesingenato isithuba elitywinwe ahambelanayo okanye ngenqindi ayikho ekwenzeni into ingqiqo nje zero akhawunti ecacileyo. I phawu luthetha yona kuqala kwavela zezibalo yamandulo eBhabhiloni izazi.

EBhabhiloni uphawu basala

Xa impucuko, wazalwa phakathi iTigris umEfrate, yasetyenziswa inkqubo ngamanani njengelifa ukusuka Sumerians amandulo. Kwaba ngokokuma - amanani ixabiso zixhomekeke bumilo yento ngokunxulumene amanye amanani. Yenzelwe iminyaka 4-5 eliwaka BC. e., kuba yayakhiwe phezu inani 60. Le izibalo esisetyenziswa ngeenkwenkwezi yamandulo baseBhabhiloni kunye iinjineli ziye wakhangela kakhulu enkulu kangaka ubenetloni. Ukuze ukusingatha ngempumelelo amanani, kwakuyimfuneko ukuba ngentloko okanye ukugcina phambi kwamehlo phindo zonke amanani ukusuka ku-1 ukuya kuma-60.

Digital zero okanye umqondiso, ukubonisa obhobhozayo baseBhabhiloni wafumana wabonakala njengoko iseti ezimbini nesinqumka engile egqithe okanye notolo. Olu phawu iye yaba yinxalenye yaye abazange bathathe inxaxheba kwimisebenzi yokalo emileyo - Ukongeza okanye siphinda-phinde ngo kwakungelula.

zero phesheya

Nokuba zezibalo zakho eMesopotamiya Zero yavela amaNdiya Central America - Maya Inca. Common kuzo zombini inkqubo nani ukuba abazange ukuphuhlisa ingcamango zero njenge nani.

Drevneamerikanskaya impucuko ushiye ihlabathi eninzi impumelelo kwinkalo ngokwasengqondweni. inkqubo Complex yamaMaya ikhalenda kunye Inca - isiphumo eminyaka amava Imigqaliselo ngeenkwenkwezi izibalo ezintsonkothileyo izibalo. Kodwa akwenzeki quadratic zabo, inani zero akakho njenge inani eziphembelela ngesiphumo imisebenzi zezibalo.

look antique

Ilifa ezingundoqo ezi zezibalo zamandulo zamaGrike waba impumelelo zabo geometry kunye ngeenkwenkwezi. Amanani e-ntetho zabo - ngaba ziqwempu ukuba abe isiqalo, isiphelo kunye nobude kwangaphambili. Zero - inani elo azifumaneki kulo mzekelo, ukubaluleka. Yeengcandelo ngobude zero kwimathematika zamandulo bulumko akwenzi ngqiqo.

Enye iinkolelo eziphambili imfundiso Aristotle kukuba ibinzana Imvelo abhorret ezincamathelayo - "Indalo ilisikizi cleaner." Infinity, ukuba yize, non-ubukho - ezi ndidi musa angena indalo yamandulo. Ngoko ke, intsingiselo mihla umbuzo othi "yintoni inani ngu 0" wayengekho onokulufikelela ukuba noArchimedes, Pythagoras okanye Euclid, nangona ezifana isimboli iqanda ifumaneka amacwecwe ngeenkwenkwezi enkulu uPtolemy. Letter "Omicron" (unobumba wokuqala οὐδέν elithi - "nto"), uya kuvela kwi zingabinanto iiseli.

Homeland zero - India

Ziziphi zezibalo Indian yasungulwa? Mahavira (850), Brahmagupta (1114), Aryabhata (476) - umbhali lo mbhalo, leyo kakhulu esezantsi ethathe imilo inkqubo mihla lokubhala kunye nemigaqo lwabo lwabasaqala arithmetic. Ababhali-mbali bakholelwa ukuba le nkqubo wokugqibela sele abolekwe i-Chinese amaIndiya, kunye nohlobo indawo yayo - ukusuka baseBhabhiloni. Kukholelwa ukuba isimboli zero kwakhona ukubolekwa amaNdiya umsebenzi kwePtolemy.

Sezibalo wokuqala uqulunqe inkqubo epheleleyo lwamanani, leyo isekhona kwaye yenza inxalenye enkulu yabantu, yaba Mohammed Bin Musa Khwarizmi (787-850), owayehlala Baghdad. In "Book of akhawunti Indian 'yakhe Amanani Arabic asithoba ichazwe ngokwenkcukacha uze uphendule lo mbuzo:" Ngaba inani 0? " Chaza zero kule ncwadi ungowokuqala. inguqulo yesiLatini yalo msebenzi, iye kabanzi eYurophu ngenkulungwane XII waza wabeka isiseko ukusasazeka ulwazi empumalanga zezibalo.

Ngokungafaniyo baseYurophu, unaphakade kwi zobulumko kwimpuma zashiy. Ngoko ke, lo zero kwi quadratic zezazinzulu Indian bamandulo nje ube luphawu sokugqibela yokunqongophala kweeyunithi abakwizikhundla ahambelanayo, kodwa inani yendalo, echaphazela result ukubala. Ukongeza zero, phinda ngo-0 - konke oku sele ufumene ixabiso imisebenzi zezibalo lebyi.

amanani yokubhala ezingeyomfuneko ukusuka ku-1 ukuya 0 iye yazuza inkangeleko sokugqibela siyabulela kuye azibhala zamandulo Indian zemathematika, kwaye abalinganiswa, yintoni ekuthiwa Arabic eYurophu, i-Arabhu kuthiwa Indiya.

Imbali Inani "zero" kubonakaliswe etymology yamagama ezisisiseko zemathematika. Igama elithi "ngesazobe" uye iingcambu Arabic kwaye sisuka kwigama elithi "al-Sifre," elithetha "engenanto, zero." IsiNgesi "zero" "marshmallow" akuphuhlanga kakuhle efanayo - umoya wasempumalanga - ivela eMpuma ukuya eYurophu kugqityezelwe, inkqubo inani esinengqiqo lula.

Amanani Arabhu eYurophu

Enye abakhuthaza kwenkqubo digital yaseYurophu Arab yaba Italian yezibalo odumileyo Leonardo Fibonacci. umsebenzi wakhe "Book Abaci" (1202) wazisa izazinzulu yaseYurophu kunye neesimboli kunye nemigaqo ngayo Arabhu babhale imisebenzi zezibalo. Lula lokuqala kunye nemodeli lweMathematika nengqiqo mpuma nok abo abaqhele unyango yonke imihla ngamanani - kubananisi kunye abarhwebi. Bakhawuleza owamkelwe ngabarhwebi Arab ukubala inkqubo nokubhala amanani. Kodwa kulo mkhuba zenzululwazi e-Europe olu lwazi nime kuphela kwinkulungwane yesi-4, ngokubuyisela ukwamkelwa zezibalo yaseYurophu kwinkqubo yamandulo.

Kuye yazuza ukubaluleka kunye nokuqaliswa a zero ekusetyenzisweni kwe-buxande yenzululwazi nokulungelelanisa inkqubo, ecetywayo kwinkulungwane XVII Rene Descartes. Zero zilahlwa kwi ziko, ixabiso wazuza ezibonakalayo kunye abangaboni iyaqondakala reference indawo yee-asi ezintathu.

ERashiya wazisa a zero kumalinge practice Leontiya Magnitskogo, umbhali adumileyo incwadi "Izibalo, oko kukuthi i-nani isayensi" (1703).

izakhiwo zero

Zero, leyo demarcates zombini amanani akhabayo kunye navumelanayo, anazo iipropati ezikhethekileyo zezibalo. It is an inani, akuyona inombolo ukuba uphawu oluvumelanayo. Ukudibanisa nokuthabatha ngeqanda ngeqanda aluchaphazeli inani nande ngo-0 unika zero. Division ngu zero uthathwa umsebenzi ingento, nto leyo kwimeko uphumezo enokubangela umonakalo elibalulekileyo inkqubo inkqubo yekhompyutha.

Yaba ngenzame kuwabela 0 waba kwindawo ukusilela kwinkqubo yekhompyutha ye-US Navy Cruiser "Yorktown", owenzeka ekwindla ka-1997 kwaye kwakhokelela ukuvalwa engagunyaziswanga kwinkqubo isimiso. Ngokungachanekanga enxulumene inani, elithetha "nto", wenze noweenqanawa zokulwa onamandla ekujoliswe awubi zokubhala.

Ixabiso eli nani lenyuka ngokubalulekileyo kuphuhliso yenzululwazi. Zero kwenzeka kwiindawo hayi nje kuphela zemathematika. Ukuva embundwini umsindo iba 0. Leliphi inani ekuqaleni isikali izixhobo yokulinganisa ezininzi, eyaziwa kunye yesikolo: 0 kwi Celsius - qhwa amanzi, ekuqalekeni ngokubala yezide - cwaka zero njalo njalo ..

iinombolo Binary, leyo wakhonza njengesiseko ekudalweni izixhobo becomputing yeli i inkqubo inani ngokokuma nesinqe ezimbini. Oku kuthetha ukuba yonke idatha wangena kwinkqubo yekhompyutha, ukuba beminwe yi indibaniselwano abalinganiswa ababini - omnye no zero.

Indima kwihlabathi yanamhlanje iikhompyutha uba isigqibo kuzo zonke iinkalo zobomi yaye, ke ngoko, imbali inani zero, ngaphandle apho imbonakalo yazo ibiya kuba akunakwenzeka, uyaqhubeka.