Inombolo yegolide engu-0, ukunikezwa kwe-3D kwenombolo enguziro eyenziwe ngegolide enomfanekiso ohlukanisiwe kungemuva elimhlophe.
Inombolo enguziro, leso sibalo esisisebenzisayo uma sikhuluma ngokungabi nalutho noma ukungabi nalutho. Uyazi ukuthi ubani owethule umbono wenombolo ethi ziro noma kungani sisebenzisa inombolo engenalo inani?
indaba yomqondo
Inombolo enguziro isetshenziswe isikhathi eside, nakuba iyinombolo engenalo inani, futhi isetshenziswa kuwo wonke amasiko. Uma sifuna ukusho ukungabibikho noma ukuntuleka kwento ethile sisebenzisa uphawu lweziro. Amagama anjengokuthi "angenalutho" noma "akukho lutho" kunzima ukuwacabanga, okuwenza abe 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 u-ziro emisebenzini eminingi futhi siyisebenzise njengegama elifanayo elithi "lutho," kodwa kufanele sikhumbule ukuthi u-zero akakaze abe khona phakade. Ngokwesibonelo, amaRoma asendulo noma amaGreki asendulo ayengasebenzisi uziro. Ayethuthuke kakhulu ezibalweni nasekufundeni izinkanyezi, ebala imiqulu ngisho nokubikezela indawo eqondile yezinkanyezi, kodwa konke lokhu akwenza ngaphandle koziro. Uma izibalo ezibalulekile kangaka zingenziwa ngaphandle kokusebenzisa lolu phawu, kungani lwethulwa 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 ukuze zibhekisele kulokho manje esikwazi ngokuthi "zero." Kodwa masingacabangi ukuthi lokhu kusetshenziswa kudlule kufilosofi kuye kwizibalo ngezinsuku ezimbalwa. Ngaphezu kwalokho, ukusetshenziswa kwegama elithi sunya kwaqala ngesiyalo esingakaxoxi, uhlelo lolimi, futhi kwakuphakathi kwekhulu lesi-5 nelesi-2 BC. Kungaleso sikhathi lapho uPanini kanye noPingala, izazi zohlelo lolimi zangaleso sikhathi, basebenzisa uphawu olufana kakhulu noziro esiwaziyo namuhla, nakuba kwakungewona uziro njengenombolo, kodwa njengohlamvu. Futhi babelisebenzisa uma bekhuluma ngento engaveli.
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 kwakuyinto evamile yosuku. Ngalé kombuso ka-Alexander Omkhulu, khona kanye endaweni emngceleni weNdiya neGrisi, imibuso yamaIndo-Greek yanda, okungukuthi, imibuso lapho kokubili amaGreki namaNdiya ayehlala khona. Amasiko amabili ahlukene ahlala endaweni eyodwa. Lokhu kwaholela ekuhlanganeni kwesiko phakathi kwamasiko womabili kuzo zonke izindawo. Ngaphezu kwalokho, 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 kukaziro njengesibambindawo encwadini yezinkanyezi i-Yavanajataka, kusukela ngekhulu lesi-3 AD. Igama lalo mbhalo ngokwalo selivele lisifundisa futhi ukuhlangana kwamasiko. Ngoba? Lona umbhalo wamaNdiya lapho igama elithi "Yavana" lisho ukuthi "Ionic" 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. Kwenzeka nini lokhu kweqa kusuka ohlelweni lolimi kuye ekubhuleni ngezinombolo?
Incwadi yokuqala lapho singathola khona uziro osetshenziswa njengenombolo yi-Brahma-sphutha-siddhanta. Lena incwadi ye-algebra eyabhalwa isazi sezibalo u-Brahmagupta ngo-628 AD. Yindawo yokuqala lapho u-zero esetshenziswa njengenombolo nalapho kuchazwa khona ukuthi lolu phawu lusetshenziswa kanjani ukwenza izibalo ngalo. Kulesi sihloko, i-zero ithatha incazelo ye-algebraic ngokuphelele.
Noma kunjalo, uziro wangaleso sikhathi wawungafani noziro wanamuhla. Isibonelo, futhi ngokuya ngencwadi ye-Brahmagupta, uma uhlukanisa 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 wayehamba njalo. 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 liye kusiLatini, i-sephirum, kwethule imiqondo emibili eYurophu: i-zero nedijithi.
Zero ezikhathini zanamuhla
Njengoba sesibonile, uziro bekungelona uphawu olulula ukulichaza ngaso sonke isikhathi. Ayikaze isetshenziswe njalo njengenombolo, kodwa ekuqaleni yayisetshenziswa njengohlamvu. Futhi ekutadisheni lolu phawu, akuzona izazi zezibalo kuphela kodwa nezazi zefilosofi nezazi zezinkanyezi ziyagqama.
Noma kunjalo, kungathiwa ukusetshenziswa kwayo njengalokhu, njengenombolo futhi njengoba siyazi namuhla, akuzange kufike kwaze kwaba ngu-1657, ezandleni zikaJohn Wallis. Ube ngowokuqala ukusebenzisa le nombolo enenani langempela (lamanje) likaziro, okusho ukuthi uma ingezwe kunoma iyiphi enye inombolo ayizange ishintshe inani layo; yahlala inguziro futhi ayizange inikele ngalutho kwelinye inani. Lo mqondo, manje esiwubona njengovamile futhi esiwusebenzisa njalo, wawunzima kakhulu ngaleso sikhathi futhi wawungaqondwa ngokugcwele.
Incazelo elula inikeze incazelo enombolweni enguziro
Kwaba ngemva konyaka lapho isazi sefilosofi nesazi sezibalo uGeorge Boole sanikeza incazelo ethile kule nombolo ngokuthi isethi yezinto inemikhawulo emibili. Umkhawulo ongaphezulu waziwa ngokuthi i-Universe futhi umkhawulo ophansi ubizwa ngokuthi lutho. Futhi kungomkhawulo ophansi, kungenalutho, lapho inombolo enguziro ihlotshaniswa. Le ncazelo ikwenze kwaba lula kakhulu ukuqonda ukuthi kungani ukungeza idijithi kuziro kubangele ukuthi leyo dijithi ihlale ingashintshile. Kungaleso sikhathi lapho abantu baphinde babona ubudlelwano noziro wezivumelwano zamaNdiya. Iqiniso lefilosofi yamaNdiya, okwakunzima kakhulu ukulihumusha noma ukuliqonda kuze kube yileso sikhathi.
Ngaphezu kwalokho, ngokulandela ithiyori emisiwe, izazi zezibalo ezinkulu ezinjengoZermelo, uCantor noVon Neumann ngokuhamba kwesikhathi zaqhubeka 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".