Inombolo yegolide engu-0, ukunikezwa kwe-3D kwenombolo enguziro eyenziwe ngegolide enomfanekiso ohlukanisiwe kungemuva elimhlophe.
Inombolo enguziro, leso sibalo esisisebenzisayo lapho sikhuluma ngokungenalutho noma lutho. Uyazi ukuthi ubani owethule umbono wenombolo ethi ziro noma kungani sisebenzisa inombolo ngaphandle kwenani?
indaba yomqondo
Inombolo enguziro isetshenziswe isikhathi eside, nakuba iyinombolo engenalo inani, futhi isetshenziswa kuwo wonke amasiko. Uma sifuna ukubheka ukungabibikho noma ukuntuleka kwento ethile sisebenzisa uphawu lweziro. Amagama anjengokuthi "akunalutho" noma "akukho lutho" kunzima ukuwacabanga futhi lokho kwenza kube yinkimbinkimbi ezingqondweni zethu.
Ingqondo yethu iyakwazi ukubona ngeso lengqondo into okungekho lutho kuyo ngaphakathi, into engenalutho ngaphakathi, into enemikhiqizo eyiziro ngaphakathi. Kodwa kunzima kakhulu ngathi ukucabanga ngomqondo "wokungenalutho" noma "ukuntuleka kokuthile" ngomqondo obanzi, ophelele.
Izibalo
Endabeni yezibalo, siyayiqonda incazelo yayo kanye nokubaluleka kwayo lapho senza izibalo kusetshenziswa izinombolo.
Uziro: ukusuka ekungabikhona kuya ekusetshenzisweni kwawo kabanzi
IGrisi neRoma
Namuhla sisebenzisa i-zero emisebenzini eminingi futhi siyisebenzise njengegama elifanayo elithi "lutho", kodwa kufanele sikhumbule ukuthi i-zero ayizange ibe khona zonke izimpilo zethu. Ngokwesibonelo, amaRoma asendulo noma amaGreki asendulo ayengasebenzisi uziro. Ayethuthuke kakhulu ezibalweni noma ekufundweni kwezinkanyezi ebala imiqulu noma ngisho nokubikezela indawo eqondile lapho izinkanyezi zingaba khona, kodwa konke lokhu bakwenza ngaphandle koziro. Uma izibalo ezibalulekile kangaka zingenziwa ngaphandle kokusebenzisa lolu phawu, kungani lwethula kamuva futhi ubani olwethule?
Uziro unezimpande zamaNdiya, futhi ukusuka lapho, waqala ukusetshenziswa emhlabeni wonke
Uma sifuna ukwazi ukuthi lolu phawu olungamele lutho luvelaphi, kumele siye eNdiya. Kumelwe sibheke ngokuqondile ifilosofi yamaBuddha namaJain. Nakuba bengakubizanga ngokuthi "zero", basebenzise igama ukuchaza leso simo "sokungenalutho", "engenalutho", "ukungabikho"... kodwa ngesi-Sanskrit yaziwa ngokuthi suyna y kha.
Izazi zezibalo zaseNdiya zasebenzisa igama elithi Sunya ukubhekisela kulokho manje esikwazi ngokuthi "zero." Kodwa masingacabangi ukuthi lokhu kusetshenziswa kudlule kufilosofi kuya kwizibalo ngezinsuku ezimbalwa. Ngaphezu kwalokho, ukusetshenziswa kwegama elithi sunya kwaqala ngesiyalo esingakaxoxi, ngohlelo lolimi, futhi kwakuphakathi kwekhulu lesi-XNUMX nelesi-XNUMX BC. Kungaleso sikhathi lapho uPanini noPingala, abahlaziyi bohlelo bangaleso sikhathi, basebenzisa uphawu olufana ncamashi noziro esiwaziyo, nakuba kwakungewona uziro njengenombolo, kodwa njengohlamvu. Futhi babelisebenzisa lapho bebhekisela entweni eyayingaveli.
I-India ne-China
Akwaziwa kahle ukuthi yethulwa nini ngoba imibhalo yomlando ayikho futhi akucaci kahle. Ngaphezu kwalokho, isiko lamaNdiya latholakala phakathi kwamasiko ahlukene njengamaShayina, impucuko yamaGreki kanye nabantu baseMesophothamiya. Okusho ukuthi, ingxube ebalulekile yamasiko futhi ehlanganisa iminyaka engaba ngu-400 yokungabaza kwamadokhumenti angenzi isiqalo esicacile sokusetshenziswa kweqanda kucace ngokuphelele.
Isibonelo, e-China basebenzisa isisekelo se-10, lapho kuvela khona i-zero, kodwa kulokhu kwakungenayo leyo ncazelo yokungabi nalutho noma lutho. Noma kunjalo, basebenzise amathebula okubala akhiwe amakholomu amaningana futhi ikholomu eyayingenalutho kwakuyikholomu enguziro.
i-indiya ne-Greece
Ukushintshana ngamasiko phakathi kweNdiya neGreece kwakuwukulandelana kosuku. Ngalé kombuso ka-Alexander Omkhulu, khona kanye endaweni yomngcele ophakathi kweNdiya neGrisi, imibuso yama-Indo-Greek yanda, okungukuthi, imibuso lapho kokubili amaGreki namaNdiya ayehlala ndawonye. Amasiko amabili ahlukene ahlala ndawonye endaweni eyodwa. Lokhu kwakusho ukuthi kwakukhona ukuhlangana kwamasiko phakathi kwamasiko womabili kuzo zonke izindawo. Futhi, sikhuluma ngamasiko amabili ayebusa kwezohwebo futhi ayengabacabangi abakhulu.
Kulokhu, amaGreki anikeza amaNdiya izincwadi zezinkanyezi lapho kubonakala khona uphawu olufana no-zero, uphawu amaNdiya ayelufunde kubantu baseMesopotamiya. Lolu phawu lwalusebenza ngaleso sikhathi njengesimeli ukukhombisa izinombolo.
isiko fusion
Singathola, isibonelo, ukusetshenziswa kwe-zero njengophawu lwendawo ku-Yavanajataka i-astronomical treatise, kusukela ngekhulu le-XNUMX AD. Igama lesivumelwano ngokwalo selivele lisifundisa futhi mayelana nokuhlangana phakathi kwamasiko. Kungani? Lona umbhalo wamaNdiya lapho igama elithi "yavana" lisho "i-Ionian" futhi, lisho "isiGreki."
Uziro wezibalo
Kuze kube manje sesibonile ukuthi uphawu lweziro lwalusetshenziswa kodwa njengophawu lwegrama ukuze lubonise ukungabi nalutho noma ukungabikho kwento ethile, kodwa hhayi njengenombolo, njengoba siyazi. Ukwenze nini lokhu kweqa kusuka kuhlelo lolimi kuya kunumerology?
Incwadi yokuqala lapho singathola khona u-zero esetshenziswa njengenombolo yi-Brahma-sphutha-siddhanta. Kuyincwadi ye-algebra eyabhalwa isazi sezibalo u-Brahmagupta ngo-628 AD. Yisizinda sokuqala lapho u-zero asetshenziswa khona njengenombolo futhi lapho kuchazwa khona ukuthi lolu phawu lusetshenziswa kanjani ukwenza izibalo ngalo. Kulesi sihloko, iqanda lithatha umqondo we-aglebraic ngokuphelele.
Noma kunjalo, i-zero yangaleso sikhathi yayingafani neyamanje. Isibonelo, futhi ngokuvumelana nencwadi ka-Brahmagupta, uma uhlukanise inombolo ngoziro, umphumela otholiwe wawuyinombolo, inani elikhulu kakhulu kodwa inani elinganqunyelwe. Ngakho-ke, bekuyinombolo, enenani elihlobene.
kusukela empumalanga kusiya entshonalanga
Nalapha imibono nokuhlakanipha kwabanye abantu kudluliselwa kwabanye. Kulokhu igama elithi sunya lishintshwa libe yi-sifr kodwa liphinde lisebenzise ukuchaza ukungabi nalutho noma ukungabikho, u-zero. Kulokhu kufanele sihambe siye edolobheni laseBaghdad, maphakathi nekhulu lesi-IX AD. Khawarizmi Persian, owaziwa kangcono ezikhathini zasendulo ngokuthi u-Algorismus, wabhala incwadi ethi On Indian Calculation esekelwe ezindabeni zaseNdiya zesayensi yezinkanyezi. Futhi nguye kanye owahumusha igama elithi sunya ngo-sifr. Igama elehlukile elinencazelo efanayo.
Futhi uLeonardo Fibonacci, indodana yesikhulu sempahla yasePisan, uyena owasakaza ngempela lezi zindlela zokubala ezazivela eMpumalanga ngoba wahamba engami. Eqinisweni, yilesi Ntaliyane esethula uphawu lweziro emazweni aseYurophu. Ngo-1192 wabhala incwadi ethi Liber Abaci, lapho echaza khona ukuthi kwasetshenziswa izinombolo eziyisishiyagalolunye kanye nophawu olukhethekile. Ukuhunyushwa kwegama elithi sifr lisuka kusi-Arabhu liyiswa kusiLatini, i-sephirum, kwethulwe e-Europe imiqondo emibili efana noziro nedijithi.
Zero ezikhathini zanamuhla
Njengoba sesibonile, uziro bekungelona uphawu olulula ukulichaza ngaso sonke isikhathi. Ayikaze isetshenziswe njalo njengenombolo, kodwa ekuqaleni yayisetshenziswa njengohlamvu. Futhi akuzona izazi zezibalo kuphela kodwa nezazi zefilosofi nezazi zezinkanyezi ziyagqama ekutadisheni lolu phawu.
Noma kunjalo, kungathiwa ukusetshenziswa njengalokhu, njengenombolo nanjengoba sisazi namuhla, akuzange kufike kwaze kwaba unyaka ka-1657, ezandleni zikaJohn Wallis. Ube ngowokuqala ukusebenzisa le nombolo enenani langempela (lamanje) lika-zero, okungukuthi, uma ingezwe kunoma iyiphi enye inombolo ayizange ishintshe inani layo, isenguziro futhi ayifaki lutho kwelinye inani. Ayizange isebenze ekuguquleni enye inombolo. Lo mqondo manje esiwubona njengovamile futhi esiwusebenzisa njalo, ngaleso sikhathi wawunzima kakhulu, wawungaqondwa ngokugcwele.
Incazelo elula inikeze incazelo enombolweni enguziro
Kwaba eminyakeni embalwa kamuva lapho isazi sefilosofi nesazi sezibalo uGeorge Boole sabeka umqondo othile kule nombolo ngokuthi iqoqo lezinto linemikhawulo emibili. Umkhawulo ophezulu owaziwa ngokuthi i-Universe kanye nomkhawulo ophansi obizwa ngokuthi lutho. Futhi ifika emkhawulweni ophansi, lutho, lapho inombolo engu-zero ihlotshaniswa khona. Le ncazelo ikwenze kwaba lula kakhulu ukuqonda ukuthi kungani ukungeza idijithi kuziro kungabangela leyo dijithi ukuthi ihlale ifana. Kungaleso sikhathi lapho abantu baphinde babona ubudlelwano obabukhona noziro wezivumelwano zamaNdiya. Iqiniso lefilosofi yamaNdiya, okwakunzima kakhulu ukulihumusha noma ukuliqonda kuze kube yileso sikhathi.
Ngaphezu kwalokho, ngokulandela ithiyori emisiwe, kamuva ochwepheshe bezibalo abakhulu abafana no-Zermelo, uCantor noma u-Von Neumann baqhubeka nokufunda inani likaziro kulawa masethi ngisho nalokho okwakwaziwa ngokuthi isethi engenazo izici.
Ziro namuhla
Njengamanje, ingabe siyazi ngempela ukuthi kusho ukuthini inani elinguziro? Nokho, impendulo, ngisho noma kubonakala sengathi amanga kithi, akunjalo neze. Sizobe sesikuzwisisile ngokwemodeli esiyikhethayo. Singaliqonda ngokuphelele inani likaziro emkhakheni wetiyori emisiwe, emkhakheni wezibalo. Ngaphezu kwalokho, siyisebenzisa njalo futhi sikwenza ngaphandle kokungabaza le nombolo. Nokho, emkhakheni wefilosofi siye sashiywa. Mayelana nalokhu, kusenempikiswano mayelana nenani elithi "lutho".