Ndarama nhamba 0, 3D inopa nhamba zero yakagadzirwa negoridhe ine ratidziro yakaparadzaniswa nechena kumashure.
Nhamba zero, iyo nhamba yatinoshandisa kana tichitaura nezve kushaya kana chinhu. Unoziva here kuti ndiani akaunza pfungwa yenhamba zero kana nei isu tichishandisa nhamba pasina kukosha?
nyaya yepfungwa
Nhamba zero yakashandiswa kwenguva yakareba, kunyange zvazvo iri nhamba isina kukosha, uye inoshandiswa mumarudzi ose. Kana tichida kureva kusavapo kana kushaikwa kwechimwe chinhu tinoshandisa chiratidzo che zero. Mazwi akaita sekuti “hapana chinhu” kana kuti “hapana” akaoma kufungidzira uye izvo zvinoita kuti zviome kupfungwa dzedu.
Pfungwa dzedu dzinokwanisa kufungidzira chinhu chisina chinhu mukati, chinhu chisina chinhu mukati, chinhu chine zero zvigadzirwa mukati. Asi zvakatiomera zvikuru kuti tifunge mupfungwa yoku“shaya chinhu” kana kuti “kushaya chimwe chinhu” mupfungwa yakafara, yakazara.
Mathematics
Panyaya yemasvomhu, tinonzwisisa zvadzinoreva uye kukosha kwadzinoita pakuita masvomhu nekushandisa manhamba.
Zero: kubva pakusavapo kusvika pakushandiswa kwakapararira
Girisi neRoma
Nhasi tinoshandisa zero mumabasa akawanda uye tinotoishandisa sechirevo che "hapana", asi tinofanira kuyeuka kuti zero haisati yavapo hupenyu hwedu hwose. Somuenzaniso, vaRoma vekare kana kuti vaGiriki vekare vakanga vasingashandisi zero. Vakanga vafambira mberi zvikuru mumasvomhu kana kuti kuongorora nyeredzi vachiverenga mavhoriyamu kana kutofanotaura nzvimbo chaiyo iyo nyeredzi dzaigona kuva, asi vakaita zvose izvi pasina mazero. Kana kuverenga kwakakosha kwakadaro kuchigona kuitwa pasina kushandisa chiratidzo ichi, nei kuchisuma gare gare uye ndiani akazvisuma?
Zero ine midzi yeIndia, uye kubva ipapo, yakatanga kushandiswa pasi rose
Kana tichida kuziva kuti chiratidzo ichi chinomiririra hapana chinobva kupi, tinofanira kuenda kuIndia. Tinofanira kutarisa zvakananga kuBuddhist neJain philosophy. Kunyangwe vasina kuidaidza kuti "zero", vakashandisa izwi kuratidza kuti "hapana", "isina chinhu", "kusavapo"... asi iyo muchiSanskrit yaizivikanwa sekuti " suyna y haha.
Vachenjeri vemasvomhu vekuIndia vakashandisa izwi rekuti Sunya kureva zvatava kuziva se "zero." Asi ngatisafunge kuti kushandiswa uku kwakapfuura kubva kuhuzivi kuenda kusvomhu mumazuva mashoma. Uyezve, kushandiswa kwezwi rokuti sunya kwakatanga muchirango chatisati takurukura, girama, uye yaiva pakati pezana remakore rechishanu nerechipiri BC. Ipapo ndipo apo Panini naPingala, vaongorori vegirama venguva iyoyo, vakashandisa chiratidzo chakada kufanana ne zero yatinoziva, kunyange zvazvo yakanga isiri zero senhamba, asi setsamba. Uye vairishandisa pavaitaura nezvechimwe chinhu chakanga chisingaoneki.
Indian uye Chinese
Hazvinyatsozivikanwa kuti rakatanga rini chaizvo nekuti magwaro enhoroondo haapo uye hazvina kujeka. Pamusoro pezvo, tsika dzechiIndia dzakawanikwa pakati petsika dzakasiyana senge maChinese, budiriro yeGreek uye vanhu veMesopotamia. Kureva kuti, musanganiswa wetsika wakakosha uye unobatawo mamwe makore 400 ekusava nechokwadi kwezvinyorwa izvo zvisingaite kuti kutanga kwakajeka kwekushandiswa kwe zero kuve pachena.
Semuenzaniso, muChina vakashandisa base 10, umo zero yakaonekwa, asi munyaya iyi yakanga isina izvo zvinoreva kusava nechinhu kana kuti hapana. Kunyange zvakadaro, vaishandisa matafura ekuverenga akaumbwa nemakoramu akati wandei uye koramu yaive isina chinhu yaive zero column.
India neGreece
Kutsinhana kwetsika pakati peIndia neGreece ndiyo yakanga iri nhevedzano yezuva racho. Mhiri kwoumambo hwaAlexander Mukuru, munharaunda chaimo yomuganhu pakati peIndia neGreece, umambo hweIndo-Greek hwakakura, ndiko kuti, umambo umo vose vari vaviri vaGiriki namaIndia vaigara pamwe chete. Tsika mbiri dzakasiyana dzinogara pamwechete panzvimbo imwe. Izvi zvaireva kuti pakanga paine mubatanidzwa wetsika pakati petsika dzose dziri mbiri munzvimbo dzose. Zvakare, tiri kutaura nezve tsika mbiri dzaitonga kutengeserana uye dzaive mafungire makuru.
Muchiitiko ichi, vaGiriki vakapa maIndia maitiro ekuongorora nyeredzi umo chiratidzo chakafanana ne zero chakaonekwa, chiratidzo icho maIndia akanga adzidza kubva kuvanhu veMesopotamia. Ichi chiratidzo chakashanda panguva iyoyo sechibatiso kuratidza nhamba.
tsika fusion
Tinogona kuwana, semuenzaniso, kushandiswa kwezero sechiratidzo chenzvimbo muYavanajataka yekuongorora nyeredzi, kubva muzana remakore re XNUMX. Zita rechibvumirano pacharo rinototidzidzisa zvakare pamusoro pekubatana pakati petsika. Sei? Iri igwaro reIndia umo izwi rekuti "yavana" rinoreva "Ionian" uye iro, zvakare, rinoreva "chiGiriki."
Masvomhu zero
Kusvikira zvino taona kuti zero chiratidzo chaishandiswa asi sechiratidzo chegirama kuratidza kusava nechinhu kana kusavapo kwechimwe chinhu, asi kwete senhamba, sezvatinoiziva. Wakaita rinhi kusvetuka kubva pagirama kuenda kunhamba?
Chinyorwa chekutanga chatinogona kuwana zero ichishandiswa senhamba ndiyo Brahma-sphutha-siddhanta chibvumirano. Ibhuku realgebra rakanyorwa nenyanzvi yemasvomhu Brahmagupta muna 628 AD. Ndiyo nzvimbo yekutanga iyo zero inoshandiswa senhamba uye panotsanangurwa kuti chiratidzo ichi chinoshandiswa sei kuita masvomhu nacho. Muchinyorwa ichi, zero inotora pfungwa yeaglebraic zvachose.
Kunyange zvakadaro, zero yenguva iyoyo yakanga isina kufanana neyazvino. Semuenzaniso, uye maererano negwaro raBrahmagupta, kana ukapatsanura nhamba ne zero, mhedzisiro yakawanikwa yaive nhamba, kukosha kukuru asi huwandu husingaverengeki. Naizvozvo, yaive nhamba, ine kukosha kwakabatana.
kubva kumabvazuva kusvikira kumavirira
Zvakare pfungwa nehuchenjeri hwevamwe vanhu hunoendeswa kune vamwe. Panyaya iyi izwi rokuti sunya rinoshandurwa kuti sifr asi richirevawo kusava nechinhu kana kusavapo, zero. Panyaya iyi tinofanira kuenda kuguta reBaghdad, pakati pezana remakore rechipfumbamwe AD. Khawarizmi Persian, aizivikanwa zviri nani kune vekare saAlgorismus, akanyora bhuku rinonzi On Indian Calculation richibva pazvinyorwa zveIndia zvekuongorora nyeredzi. Uye ndiye chaiye akadudzira izwi rokuti sunya na sifr. Izwi rakasiyana rinoreva zvakafanana.
Uye Leonardo Fibonacci, mwanakomana wePisan mukuru wetsika, ndiye akanyatso kuparadzira nzira dzekuverenga idzi dzakabva kuMabvazuva nekuti akafamba asingamire. Muchokwadi, aive muItaly uyu akaunza chiratidzo che zero kunyika dzeEurope. Muna 1192 akanyora Liber Abaci, kwaanotsanangura kuti nhamba pfumbamwe dzakashandiswa uyewo chiratidzo chinokosha. Dudziro yeshoko rekuti sifr kubva muchiArabic kuenda kuLatin, sephirum, yakaunzwa muEurope pfungwa mbiri dzakadai sezero uye digit.
Zero munguva dzazvino
Sezvataona, zero haina kugara iri chiratidzo chiri nyore kutsanangura. Haisati yagara ichishandiswa senhamba, asi yakatanga kushandiswa setsamba. Uye kwete chete masvomhu asiwo vazivi nevazivi venyeredzi vanomira pachena mukudzidza kwechiratidzo ichi.
Kunyange zvakadaro, zvinogona kutaurwa kuti kushandiswa kwakadaro, senhamba uye sezvatinoiziva nhasi, hakuna kusvika mugore ra1657, pamaoko aJohn Wallis. Ndiye akatanga kushandisa nhamba iyi ine nhamba chaiyo (yazvino) ye zero, kureva kuti, kana yakawedzerwa kune imwe nhamba haina kuchinja kukosha kwayo, yakanga ichiri zero uye haina chimwe chinhu kune imwe kukosha. Izvo hazvina kushanda kugadzirisa imwe nhamba. Iyi pfungwa yatinoona iye zvino seyakajairika uye yatinoshandisa nguva dzose, panguva iyoyo yakanga yakaoma zvikuru, yakanga isinganzwisisi zvizere.
Tsanangudzo iri nyore yakapa zvinoreva nhamba zero
Aive makore mashoma gare gare apo muzivi uye nyanzvi yemasvomhu George Boole akaisa pfungwa kune iyi nhamba nekutaura kuti seti yezvinhu ine miganhu miviri. Muganho wepamusoro unozivikanwa seUniverse uye muganho wakaderera unonzi hapana. Uye iri kumucheto wakaderera, pasina, iyo iyo nhamba zero inobatanidzwa. Tsananguro iyi yakaita kuti zvive nyore kunzwisisa kuti nei kuwedzera dijiti kune zero kuchizokonzera kuti dhijiti irambe yakafanana. Panguva iyoyo vanhu vakazivawo hukama hwaivepo ne zero yezvibvumirano zveIndia. Chokwadi chehuzivi hwechiIndia, icho kusvika panguva iyoyo chaive chakaoma kududzira kana kunzwisisa.
Uyezve, vachitevera seti dzidziso, gare gare masvomhu makuru akadai saZermelo, Cantor kana Von Neumann vakaramba vachidzidza kukosha kwezero mumaseti aya uye kunyangwe zvaizivikanwa seti isina zvinhu.
Zero nhasi
Parizvino, tinoziva here kuti zero kukosha zvinorevei? Zvakanaka, mhinduro, kunyange kana zvichiita senhema kwatiri, handizvo zvachose. Tichange tazvinzwisisa maererano nemuenzaniso watinosarudza. Tinogona kunyatsonzwisisa kukosha kwe zero mumunda weiyo set theory, mundima yemasvomhu. Uyezve, tinoishandisa nguva dzose uye tinozviita pasina kupokana iyi digit. Zvisinei, mundima yehuzivi takasiiwa kumashure. Panyaya iyi, kuchine nharo pamusoro pekukosha kwe "hapana".