Ndarama nhamba 0, 3D inopa nhamba zero yakagadzirwa negoridhe ine ratidziro yakaparadzaniswa nechena kumashure.
Nhamba zero, nhamba iyoyo yatinoshandisa patinotaura nezvekusava nematuro kana kusavapo. Unoziva here kuti ndiani akaunza iyo pfungwa yenhamba zero kana nei isu tichishandisa nhamba isina kukosha?
nyaya yepfungwa
Nhamba zero yakashandiswa kwenguva yakareba, kunyange zvazvo iri nhamba isina kukosha, uye inoshandiswa mumarudzi ose. Kana tichida kureva kusavapo kana kushaikwa kwechinhu tinoshandisa chiratidzo che zero. Mazwi akaita sekuti “hapana chinhu” kana kuti “hapana” akaoma kufungidzira, izvo zvinoita kuti ave akaoma kunzwisisa mupfungwa 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 nokusingaperi. Somuenzaniso, vaRoma vekare kana kuti vaGiriki vekare vakanga vasingashandisi zero. Vakanga vafambira mberi zvikuru mumasvomhu noruzivo rwenyeredzi, vachiverenga mavhoriyamu uye kunyange kufanotaura nzvimbo chaiyo yenyeredzi, asi vakaita zvose izvi pasina mazero. Kana kuverenga kwakakosha kudaro kuchigona kuitwa pasina kushandisa chiratidzo ichi, nei chakazosumwa 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.
Nyanzvi dzemasvomhu dzekuIndia dzakashandisa shoko rokuti Sunya kureva yatinoziva iye zvino se "zero." Asi ngatisafunge kuti kushandiswa uku kwakapfuura kubva kuhuzivi kuenda kusvomhu nemazuva mashoma. Pamusoro pazvo, kushandiswa kwezwi rokuti sunya kwakatanga muchirango chatisati takurukura, girama, uye paive pakati pezana ramakore rechishanu nerechipiri BC. Ipapo ndipo apo Panini naPingala, vaongorori vegirama venguva iyoyo, vakashandisa chiratidzo chakada kufanana nezero yatinoziva nhasi, kunyange zvazvo yakanga isiri zero senhamba, asi setsamba. Uye vairishandisa pavaitaura nezvechimwe chinhu chisingaonekwe.
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 ndizvo zvaive zvave kuitika. Kupfuura umambo hwaAlexander Mukuru, munharaunda chaimo yemuganhu pakati peIndia neGreece, umambo hweIndo-Greek hwakakura, ndiko kuti, umambo umo vose vari vaviri vaGiriki namaIndia vaigara. Tsika mbiri dzakasiyana dzinogara panzvimbo imwe. Izvi zvakaita kuti pave nekubatana kwetsika pakati petsika dzose munzvimbo dzese. Pamusoro pazvo, tiri kutaura nezvetsika mbiri dzaidzora kutengeserana uye dzaive pfungwa huru.
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
Isu tinogona kuwana, semuenzaniso, kushandiswa kwezero sechibatiso mugwaro renyeredzi Yavanajataka, kubva muzana ramakore rechitatu AD. Zita rechinyorwa pacharo rinototidzidzisa zvakare kusanganiswa kwetsika. Nokuti? Iri igwaro reIndia iro izwi rekuti "Yavana" rinoreva "Ionic" uye iro, zvakare, rinoreva "chiGiriki."
Masvomhu zero
Kusvika pari zvino taona kuti chiratidzo che zero chakashandiswa asi sechiratidzo chegirama kuratidza kusava nechinhu kana kusavapo kwechinhu, asi kwete senhamba, sezvatinoiziva. Izvi zvakaitika rini kubva pagirama kuenda kunhamba?
Chinyorwa chekutanga chatinogona kuwana zero inoshandiswa senhamba ndiyo Brahma-sphutha-siddhanta chibvumirano. Ichi chinyorwa che algebra chakanyorwa nenyanzvi yemasvomhu Brahmagupta muna 628 AD. Ndiyo nzvimbo yekutanga iyo zero inoshandiswa senhamba uye painotsanangurwa kuti chiratidzo ichi chinoshandiswa sei kuita masvomhu nacho. Muchinyorwa ichi, zero inotora zvinoreva algebraic zvakazara.
Zvakadaro, zero yenguva iyoyo yakanga isina kufanana nezero yanhasi. Semuyenzaniso, uye zvinoenderana negwaro raBrahmagupta, kana ukapatsanura nhamba ne zero mhedzisiro yakawanikwa yaive nhamba, kukosha kukuru asi kwehuwandu 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 anoona nezvetsika, ndiye akanyatso kuparadzira nzira dzekuverenga idzi dzakabva kuMabvazuva nekuti aifamba nguva dzose. Muchokwadi, aive muItaly uyu akaunza chiratidzo che zero kunyika dzeEurope. Muna 1192 akanyora Liber Abaci, kwaanotsanangura kuti nhamba pfumbamwe dzakashandiswa uyewo chiratidzo chinokosha. Kushandurwa kweshoko rekuti sifr kubva muchiArabic kuenda kuLatin, sephirum, kwakaunza pfungwa mbiri muEurope: zero 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.
Kunyangwe zvakadaro, zvinogona kutaurwa kuti kushandiswa kwayo sekudaro, senhamba uye sezvatinoiziva nhasi, hakuna kusvika kusvika 1657, pamaoko aJohn Wallis. Ndiye akatanga kushandisa nhamba iyi ine nhamba chaiyo (yazvino) ye zero, kureva kuti kana yakawedzerwa kune imwe nhamba yaisashandura kukosha kwayo; yakaramba iri zero uye haina kupa chero chinhu kune imwe kukosha. Pfungwa iyi, yatinoona seyakajairika uye yatinoshandisa semazuva ese, yakanga yakaoma panguva iyoyo uye yakanga isinganyatsonzwisiswi.
Tsanangudzo iri nyore yakapa zvinoreva nhamba zero
Rakanga riri gore rakatevera apo muzivi uye nyanzvi yemasvomhu George Boole akapa imwe chirevo kunhamba iyi nokutaura kuti seti yezvinhu ine miganhu miviri. Muganho wepamusoro unozivikanwa seUniverse uye muganho wakaderera unonzi hapana. Uye zviri nechepasi muganhu, pasina chinhu, iyo nhamba zero inobatanidzwa. Tsananguro iyi yakaita kuti zvive nyore kunzwisisa kuti nei kuwedzera dhijiti kune zero kwakakonzera kuti dhijiti irambe isina kushanduka. Yakanga iri nguva iyo vanhu vakazivawo hukama ne zero yezvibvumirano zveIndia. Chokwadi chehuzivi hwechiIndia, icho kusvika panguva iyoyo chaive chakaoma kududzira kana kunzwisisa.
Uyezve, vachitevera seti dzidziso, nyanzvi dzemasvomhu dzakaita seZermelo, Cantor naVon Neumann vakazoenderera mberi vachidzidza kukosha kwezero mumaseti aya uye kunyangwe zvaizivikanwa seti isina maelementi.
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".