Inombolo yegolide engu-0, unikezelo lwe-3D lwenani elinguziro elenziwe ngegolide elinomboniso obekwe wodwa kwimvelaphi emhlophe.
Inani elingu-zero, elo nani esilisebenzisayo xa sithetha ngokungabikho okanye nto. Ngaba uyazi ukuba ngubani owazisa umbono wenombolo zero okanye kutheni sisebenzisa inani ngaphandle kwexabiso?
ngumcimbi wengqondo
Inani elingu-zero lisetyenziswe ixesha elide, nangona linani elingenaxabiso, kwaye lisetyenziswa kuzo zonke iinkcubeko. Xa sifuna ukubhekisa kukungabikho okanye ukungabikho kwento ethile sisebenzisa isimboli esingu-zero. Amagama afana nelithi "akukho nto" okanye "akukho nto" kunzima ukuwacinga kwaye oko kwenza ukuba ingqondo yethu ibe nzima.
Ingqondo yethu iyakwazi ukucinga into ekungekho nto ngaphakathi, into engenanto ngaphakathi, into eneemveliso zero ngaphakathi. Kodwa kunzima kakhulu kuthi ukucinga ngengqiqo "engenanto" okanye "ukungabikho kwento" ngokubanzi, ingqiqo epheleleyo.
IMathematika
Kwimeko yemathematika, siyayiqonda intsingiselo yayo kunye nokubaluleka kwayo xa kusenziwa izibalo kusetyenziswa amanani.
U-zero: ukusuka ekungabinikho ukuya ekusetyenzisweni kwayo ngokubanzi
IGrisi neRoma
Namhlanje sisebenzisa i-zero kwimisebenzi emininzi kwaye siyisebenzise njengesithethantonye esithi "akukho nto", kodwa kufuneka sikhumbule ukuba i-zero ayizange ibekho ubomi bethu bonke. Ngokomzekelo, amaRoma amandulo okanye amaGrike amandulo ayengalisebenzisi elithi zero. Babehambele phambili kakhulu kwimathematika okanye ekuvumiseni ngeenkwenkwezi ebala imiqulu okanye bade baxele kwangaphambili indawo eziya kuba kuyo iinkwenkwezi, kodwa bakwenza konke oku ngaphandle kwamaqanda. Ukuba izibalo ezibaluleke ngolo hlobo zinokwenziwa ngaphandle kokusebenzisa olu simboli, kwakutheni ukuze lwazise kamva yaye ngubani owaluzisayo?
Uziro uneengcambu zamaIndiya, kwaye ukusuka apho, wasetyenziswa kwihlabathi liphela
Ukuba sifuna ukwazi ukuba luvela phi olu phawu lungamelanga nto, kufuneka siye eIndiya. Kufuneka sijonge ngokuthe ngqo kwifilosofi kaBuddha kunye neJain. Nangona bengayibizanga ngokuthi "zero", baye basebenzisa igama ukuchaza eso simo "sokungenanto", "engenanto", "ukungabikho"... kodwa ngesiSanskrit yayisaziwa ngokuba suyna y kha.
Izilumko zemathematika zaseIndiya zasebenzisa igama elithi Sunya ukubhekisa kwinto esiyaziyo ngoku njenge "zero." Kodwa masingacingi ukuba oku kusetyenziswa kudlule kwifilosofi ukuya kwimathematika kwimiba yeentsuku. Ngaphezu koko, ukusetyenziswa kwegama elithi sunya kwaqala kwingqeqesho esingekayixoxi, igrama, kwaye yayiphakathi kwenkulungwane yesi-XNUMX neye-XNUMX BC. Kwaba ngelo xesha apho uPanini kunye noPingala, abahlalutyi begrama belo xesha, basebenzisa isimboli esifana kakhulu no-zero esiwaziyo, nangona kwakungekho zero njengenani, kodwa njengeleta. Yaye babelisebenzisa xa bebhekisela kwinto engabonakali.
India kunye China
Akwaziwa ukuba yaqalwa nini na kuba amaxwebhu embali angekho kwaye akucaci. Ukongeza, inkcubeko yamaIndiya yafunyanwa phakathi kweenkcubeko ezahlukeneyo ezifana neTshayina, impucuko yamaGrike kunye nabantu baseMesopotamiya. Oko kukuthi, umxube obalulekileyo wenkcubeko kwaye oquka iminyaka engama-400 yamathandabuzo abhaliweyo angenzi isiqalo esicacileyo sokusetyenziswa kwe-zero kucace ngokupheleleyo.
Ngokomzekelo, e-China basebenzisa isiseko se-10, apho i-zero ibonakala khona, kodwa kule meko yayingenayo loo ntsingiselo yokungabi nanto okanye akukho nto. Nangona kunjalo, basebenzisa iitheyibhile zokubala ezenziwe ngamakholomu amaninzi kwaye ikholamu eyayingenanto yayiyikholomu ye-zero.
Indiya kunye neGrisi
Utshintshiselwano ngenkcubeko phakathi kweIndiya neGrisi yayiyeyona nto iphambili. Ngaphaya kobukhosi buka-Aleksandire Omkhulu, kanye kummandla womda ophakathi kweIndiya neGrisi, kwakhula izikumkani zamaIndo-Greek, oko kukuthi, izikumkani apho amaGrike namaIndiya ayehlala kunye. Iinkcubeko ezimbini ezahlukeneyo zihlala kunye kwindawo enye. Oku kwakuthetha ukuba kukho ukudityaniswa kwenkcubeko phakathi kweenkcubeko zombini kuzo zonke iindawo. Kwakhona, sithetha ngeenkcubeko ezimbini ezazilawula urhwebo kwaye zaziziingqondi ezinkulu.
Kule meko, amaGrike anikezela amaNdiya ngeenkwenkwezi zeenkwenkwezi apho kwavela khona isimboli esifana ne-zero, isimboli amaNdiya ayefunde kubantu baseMesopotamiya. Olu phawu lwalusebenza ngelo xesha njengesibambi-ndawo ukubonisa amanani.
ukudibanisa inkcubeko
Sinokufumana, umzekelo, ukusetyenziswa kwe-zero njengendawo yokumakisha kwi-Yavanajataka i-astronomical treatise, ukususela kwi-AD yekhulu le-XNUMX. Igama lomnqophiso ngokwalo sele lisifundisa kwakhona malunga nokudibanisa phakathi kweenkcubeko. Ngoba? Olu luxwebhu lwaseIndiya apho igama elithi "yavana" lithetha "i-Ionian" kwaye, lithetha "isiGrike."
Uziro wezibalo
Ukuza kuthi ga ngoku siye sabona ukuba isimboli engu-zero yayisetyenziswa kodwa njengophawu lwegrama ukubonisa ukungabi nanto okanye ukungabikho kwento ethile, kodwa kungekhona njengenani, njengoko silazi. Ukwenze nini ukutsiba ukusuka kwigrama ukuya kwi-numerology?
Inqaku lokuqala apho sinokufumana i-zero isetyenziswe njengenani yiBrahma-sphutha-siddhanta. Yincwadi yealgebra eyabhalwa yingcali yezibalo uBrahmagupta ngo 628 AD Sisiza sokuqala apho u-zero usetyenziswa njengenani nalapho kuchazwa indlela olu phawu lusetyenziswa ngayo ukwenza izibalo ngalo. Kule ngxelo, i-zero ithatha intsingiselo ye-aglebraic ngokupheleleyo.
Nangona kunjalo, i-zero yelo xesha yayingafani nale yangoku. Ngokomzekelo, kwaye ngokungqinelana ne-Brahmagupta, ukuba wahlula inani nge-zero, umphumo ofunyenweyo wawuyinani, ixabiso elikhulu kakhulu kodwa inani elingapheliyo. Ngoko ke, yayiyinombolo, enexabiso elinxulumeneyo.
ukusuka empuma kuye entshona
Kwakhona iingcamango nobulumko bezinye izizwe zidluliselwa kwabanye. Kule meko igama elithi sunya liyatshintshwa libe yi-sifr kodwa likwasebenza ukubonisa ukulambatha okanye ukungabikho, u-zero. Kule meko kufuneka sihambe siye kwisixeko saseBaghdad, phakathi kwekhulu le-IX leminyaka AD. Khawarizmi Persian, owaziwa ngcono kumaxesha aphakathi njengoAlgorismus, wabhala incwadi ethi On Indian Calculation esekelwe kwiincwadi zaseIndiya zenzululwazi ngeenkwenkwezi. Kwaye inguye kanye owaguqulela igama elithi sunya ngo-sifr. Igama elahlukileyo kwintsingiselo efanayo.
Kwaye uLeonardo Fibonacci, unyana wegosa lempahla yasePisan, nguye owasasaza ngokwenene obu buchule bokubala obuvela eMpuma kuba wayehamba engayeki. Enyanisweni, ngulo mTaliyane owazisa uphawu lweziro kumazwe aseYurophu. Ngowe-1192 wabhala incwadi ethi Liber Abaci, apho achaza ukuba kwasetyenziswa amanani alithoba kunye nophawu olukhethekileyo. Ukuguqulelwa kwegama elithi sifr ukusuka kwisiArabhu ukuya kwisiLatini, i-sephirum, laziswa eYurophu iikhonsepthi ezimbini ezinjengoziro kunye nedigit.
Zero kumaxesha anamhlanje
Njengoko sele sibonile, u-zero ebengasoloko eluphawu olulula ukuluchaza. Ayizange isoloko isetyenziswa njengenani, kodwa yayisetyenziswa ekuqaleni njengonobumba. Yaye asingazo iingcali zezibalo kuphela kodwa kwanezithandi zobulumko nabavumisi ngeenkwenkwezi ababalaseleyo ekufundisiseni lo mqondiso.
Nangona kunjalo, kunokuthiwa ukusetyenziswa njengalo, njengenani nanjengoko silazi namhlanje, akuzange kufike de kube ngunyaka we-1657, ezandleni zikaJohn Wallis. Waba ngowokuqala ukusebenzisa eli nani ngexabiso lokwenyani (langoku) lika-zero, oko kukuthi, ukuba lidityaniswe nakweliphi na elinye inani alizange litshintshe ixabiso lalo, lalingu-zero kwaye alinagalelo kwanto kwelinye ixabiso. Ayikhange isebenze ukuguqula elinye inani. Le ngcamango ngoku siyibona njengento eqhelekileyo kwaye siyisebenzisa rhoqo, ngelo xesha yayinzima kakhulu, yayingaqondwa ngokupheleleyo.
Ingcaciso elula inike intsingiselo kwinani elinguziro
Kwakuyiminyaka embalwa kamva apho ifilosofi kunye nesazi sezibalo uGeorge Boole wabeka ingqiqo kweli nani ngokuthi iseti yezinto zinemida emibini. Umda ophezulu owaziwa ngokuba yi-Universe kunye nomda ophantsi obizwa ngokuba yinto. Kwaye kumda osezantsi, akukho nto, apho inani elingu-zero lidityaniswa khona. Le ngcaciso yenza ukuba kube lula ukuqonda ukuba kutheni ukongeza idijithi ku-zero kunokubangela ukuba idijithi ihlale ifana. Kungelo xesha apho abantu baqaphela ubudlelwane obukhoyo kunye ne-zero yezivumelwano zaseIndiya. Inyaniso yentanda-bulumko yamaIndiya, ekwakunzima kakhulu ukuyitolika okanye ukuyiqonda kude kube ngoko.
Ngaphaya koko, ngokulandela ithiyori iseti, kamva iingcali zezibalo ezinkulu ezifana noZermelo, uCantor okanye uVon Neumann baqhubeka befunda ixabiso lika-zero kwezi seti kwanento eyayisaziwa njengeseti engenaziqalelo.
Uziro namhlanje
Okwangoku, ngaba siyazi ngenene ukuba lithetha ukuthini ixabiso elinguziro? Ewe, impendulo, nokuba ibonakala ngathi bubuxoki kuthi, akunjalo kwaphela. Siya kuba siyiqonda ngokwemodeli esiyikhethayo. Sinokuqonda ngokugqibeleleyo ixabiso le-zero kwinkalo yethiyori eseti, kwinkalo yezibalo. Ngaphezu koko, siyisebenzisa rhoqo kwaye siyenza ngaphandle kokuthandabuza le dijiti. Nangona kunjalo, kwinkalo yefilosofi siye sashiywa ngasemva. Kulo mba, kusekho ingxoxo malunga nexabiso "lanto".