Sei tisinga patsanure ne zero?

Vaverengi vangashamisika kuti sei ini ndichipa chinyorwa chose kune yakadaro banal nyaya? Chikonzero nhamba inokatyamadza yevadzidzi (!) vachiita basa iri pasi pezita. Uye kwete vadzidzi chete. Dzimwe nguva ndinobata uye vadzidzisi. Ko vadzidzi vevadzidzisi vakadai vachakwanisa kuitei mumasvomhu? Chikonzero chekare chekunyora chinyorwa ichi yaive hurukuro nemudzidzisi uyo kupatsanurwa ne zero rakanga risiri dambudziko ...

Ne zero, hongu, kunze kwekunetseka pasina zvachose, nekuti isu hatidi chaizvo kuishandisa muhupenyu hwezuva nezuva. Hatiende kunotenga zero mazai. "Mukamuri mune munhu mumwechete" inonzwika neimwe nzira, uye "zero vanhu" inonzwika seyakagadzirwa. Nyanzvi dzemitauro dzinoti zero iri kunze kwehurongwa hwemutauro.

Tinogona kuita pasina zero mumaakaundi ebhangi zvakare: ingo shandisa - sepa thermometer - tsvuku uye bhuruu kune yakanaka uye yakaipa hunhu (ona kuti kune tembiricha zvakajairika kushandisa tsvuku kune nhamba dzakanaka, uye kumabhengi maakaundi. ndiyo imwe nzira yakatenderedza, nekuti debit inofanirwa kukonzeresa yambiro, saka tsvuku inokurudzirwa zvakanyanya).

Nekusanganisira zero senhamba yechisikigo, tinobata padambudziko rekusiyanisa Makadhinari nhamba od mhuri. Mukati me1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ....

simba renhamba rakafanana nenhamba yenzvimbo yayakamira. Zvikasadaro, yatova mukutevedzana 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, .....

Nhamba ye singleton seti inouya yechipiri, nhamba yemaseti ane zvinhu zviviri inouya yechitatu, zvichingodaro. Isu tinofanirwa kutsanangura kuti sei, semuenzaniso, isu tisingaverenge nzvimbo dzevatambi mumakwikwi kubva pakutanga. Zvino uyo anenge ahwina pekutanga aizowana menduru yesirivha (goridhe rakaenda kumunhu akunda zero), zvichingodaro. Mutambo wenhabvu wakada kufanana wakashandiswa - handizivi kana Vaverengi vachiziva kuti "league one" zvinoreva " kutevera zvakanakisisa." ", uye ligi razero rinodaidzwa kuti rive "ligi hombe".

Dzimwe nguva tinonzwa kupokana kwatinoda kutanga kubva pakutanga, nekuti yakanakira vanhu veIT. Kuenderera mberi nekufunga uku, tsananguro yekiromita inofanirwa kushandurwa - inofanirwa kunge iri 1024 m, nekuti iyi ndiyo nhamba yemabheti mu kilobyte (ini ndichataura nezve anecdote inozivikanwa kumakomputa masayendisiti: "Ndeupi musiyano uripo pakati pemunhu mutsva uye mudzidzi wesainzi yekombuta uye mudzidzi wechishanu wechikoro ichi? kuti kilobyte ndeye 1000 kilobytes, yekupedzisira - kuti kiromita 1024 metres")!

Imwe pfungwa yekuona, iyo inofanira kutotorwa zvakanyanya, ndeiyi: tinogara tichiyera kubva pakutanga! Zvakakwana kutarisa chero chiyero pamutongi, pazviyero zveimba, kunyange paawa. Sezvo tichiyera kubva paziro, uye kuverenga kuchigona kunzwisiswa sechiyero chine dimensionless unit, saka tinofanira kuverenga kubva paziro.

Inyaya iri nyore, asi...

Ngatisiyei pfungwa huru uye tidzokere kukupatsanura ne zero. Nyaya yacho iri nyore uye ingadai iri nyore dai isiri ... saka chii? Ngatifunge uye tiedze. Ingave yakawanda sei - imwe yakakamurwa ne zero? Ngationei: 1/0 = x. Wanza mativi ese nedhinominata reruboshwe.

Tinowana 1=0. Pane chakaipa! Chii chakaitika? Ah fungidzira! Iko kufungidzira kuti kune quotient yekubatana uye zero inotungamirira kune kupesana. Uye kana imwe isingagoni kukamurwa ne zero, ipapo imwe nhamba inogona. Kana, Muverengi, iwe uchikwenya mapendekete ako uye unoshamisika kuti sei munyori (ndiko kuti, ini) anonyora nezve platitudes dzakadaro, saka ... Ndinofara kwazvo!

Iyo formula 0/0 = 0 inogona kudzivirirwa pahwaro hwekusindimara, asi inopesana nemutemo wekuti mhedzisiro yekuparadzanisa nhamba pachayo yakaenzana neimwe. Zvechokwadi, asi zvakasiyana chaizvo zviratidzo zvakadai se 0/0, °/° uye zvakafanana mucalculus. Haarevi chero nhamba, asi maratidziro ezviratidzo kune mamwe mateedzana emamwe marudzi.

Mubhuku reinjiniya yemagetsi, ndakawana kuenzanisa kunonakidza: kupatsanura ne zero kune njodzi semagetsi emagetsi. Izvi zvakajairika: Mutemo weOhm unotaura kuti chiyero chemagetsi kupikisa chakaenzana nezvino: V = U / R. Kana kupikisa kwaiva zero, inoretically isingagumi ikozvino yaizoyerera kuburikidza nekondukita, ichipisa zvose zvingaita conductors.

Ndakambonyora nhetembo pamusoro pengozi yekukamura ne zero pazuva rega rega revhiki. Ndinoyeuka kuti zuva raishamisa zvikuru rakanga riri China, asi inhamo nokuda kwebasa rangu rose munharaunda iyi.

Paunogovanisa chinhu ne zero

Mangwanani-ngwanani Muvhuro

Vhiki zvichangobva kuitika

Wakatokundikana zvinosiririsa.

Kana Chipiri masikati

Unoisa zero mudhinominata

Ndichakuudza ipapo, uri kukanganisa

Nyanzvi yemasvomhu yakaipa!

Kana nepazero, kuburikidza nekutsveyamisa,

Wanna kupatsanura neChitatu

Unozopinda mumatambudziko

Une uswa nemvura mumusoro mako!

Mumwe Bartek aiva nesu.

Aipesana nemitemo.

NeChina, inoparadzaniswa ne zero.

Haachisiri pakati pedu!

Kana chishuwo chinoshamisa chavabata

Gurai ne zero neChishanu

Ndichataura chokwadi, ndichataura chokwadi:

Kutanga kwakashata kwevhiki ino.

Kana iri zero, kumwe musi weMugovera

Muparadzi achava wako (kwete kushinga)

Pfugama pasi pefenzi yechechi.

Uku ndiko kumuka kwako.

Unoda zero pasi pe dash,

Ita zororo neSvondo

Uya nechoko, bhodhi dema.

Nyora: haina kupatsanurwa ne zero!

Zero inobatanidzwa nekusava nechinhu uye kusavapo. Zvechokwadi, akauya kumasvomhu sehuwandu hwekuti, kana hwawedzerwa kune chero ipi zvayo, haichinje: x + 0 = x. Asi ikozvino zero inoonekwa mune akati wandei mamwe maitiro, kunyanya se scale kutanga. Kana kunze kwehwindo pasina tembiricha yakanaka kana chando, zvino ... iyi zero, izvo zvisingareve kuti hapana tembiricha zvachose. Zero-class monument haisi iyo yakaputswa kwenguva yakareba uye haipo. Pane zvinopesana, chinhu chakafanana neWawel, Eiffel Tower uye Statue of Liberty.

Zvakanaka, kukosha kwe zero mupositional system hakugone kuwedzeredzwa. Unoziva here, Muverengi, Bill Gates ane zero mangani muakaundi yake yekubhangi? Handizivi, asi ndinoda hafu. Sezviri pachena, Napoleon Bonaparte akacherechedza kuti vanhu vakaita sezero: vanowana zvinoreva kuburikidza nechinzvimbo. Mufirimu raAndrzej Wajda As the Years, As the Days Go by, muimbi ane shungu Jerzy anoputika: "MuFiristiya i zero, nihil, hapana, hapana, nihil, zero." Asi zero inogona kuva yakanaka: "zero kutsauka kubva pane zvakajairwa" zvinoreva kuti zvese zviri kufamba zvakanaka, uye ramba wakadaro!

Ngatidzokerei kumasvomhu. Zero inogona kuwedzerwa, kubviswa uye kuwanzwa pasina kurangwa. “Ndakawedzera zero kilograms,” Manya anodaro kuna Anya. “Uye izvi zvinonakidza, nekuti ndarasikirwa nehuremu humwe chete,” anopindura kudaro Anya. Saka ngatidye zvitanhatu zero zveice cream katanhatu, hazvizotikuvadze.

Hatigone kupatsanura ne zero, asi tinogona kupatsanura ne zero. Ndiro ye zero dumplings inogona kupihwa nyore nyore kune avo vakamirira chikafu. Mumwe nemumwe achawana marii?

Zero haisi yakanaka kana yakaipa. Izvi uye nhamba non-positiveи asiri-negative. Inogutsa kusaenzana x≥0 uye x≤0. Kupokana kwe "chimwe chinhu chakanaka" hachisi "chimwe chinhu chisina kunaka", asi "chimwe chinhu chisina kunaka kana chakaenzana ne zero". Nyanzvi dzeMasvomhu, zvinopesana nemitemo yemutauro, dzichagara dzichitaura kuti chimwe chinhu "chakaenzana ne zero" uye kwete "zero." Kururamisa tsika iyi, tine: kana tikaverenga fomula x = 0 "x i zero", zvino x = 1 tinoverenga "x yakaenzana neimwe", iyo inogona kumedzwa, asi zvakadini ne "x = 1534267"? Iwe zvakare haugone kugovera kukosha kwenhamba kune iyo 0⁰kana kusimudza zero kune simba risina kunaka. Kune rumwe rutivi, unogona kubvisa zero pakuda ... uye mhedzisiro inogara iri zero. 

Exponential function y = a^x, hwaro hwakanaka hwea, haambove ziro. Izvi zvinotevera kuti hapana zero logarithm. Chokwadi, logarithm ye a to base b ndiyo exponent iyo base inofanira kusimudzwa kuti iwane logarithm ye. Kune = 0, hapana chiratidzo chakadaro, uye zero haigone kuva hwaro hwelogarithm. Zvisinei, zero mu "denominator" yechiratidzo chaNewton chimwe chinhu. Isu tinofungidzira kuti zvibvumirano izvi hazvitungamiri kune kupokana.

uchapupu hwenhema

Kupatsanurwa ne zero inyaya yakajairika yehumbowo hwenhema, uye inoitika kunyangwe kune vane ruzivo rwemasvomhu. Rega ndikupe mienzaniso miviri yandinofarira. Yokutanga ndeye algebraic. Ndicha "prover" kuti nhamba dzese dzakaenzana. Ngatitii pane nhamba mbiri dzisina kuenzana. Naizvozvo, chimwe chazvo chikuru pane chimwe, regai a > b. Ngatitorei kuti c ndiwo musiyano wavo

c \uXNUMXd a - b. Saka isu tine - b = c, kubva a = b + c.

Isu tinowanza zvikamu zviviri zvekupedzisira ne-b:

a² – ab = ab + ac – b2 – bc.

Ndinoturikira ak kuruboshwe, hongu ndinorangarira nezvekuchinja chiratidzo:

a² - ab - ac = ab - b2 - bc.

Ini handisanganisi zvinhu zvinowanzoitika:

A (a-b-c) \uXNUMXd b (a-b-c),

Ini ndinogovana uye ndine zvandaida:

a = b.

Uye chaizvoizvo kunyange mutorwa, nokuti ndakafunga kuti a > b, uye ndakawana kuti a = b. Kana mumuenzaniso uri pamusoro pe "kubiridzira" zviri nyore kuziva, zvino muuchapupu hwejometri pasi apa hazvisi nyore. Ini ndicharatidza kuti ... iyo trapezoid haipo. Nhamba inowanzonzi trapezoid haipo.

Asi ngatiti kutanga kune chinhu chakadai se trapezoid (ABCD mumufananidzo uri pasi apa). Iine mativi maviri anoenderana ("mabhesi"). Ngatitambanudze mabhesi aya, sezvakaratidzwa mumufananidzo, kuti tiwane paralelogiramu. Diagonal dzayo dzinopatsanura imwe diagonal ye trapezoid kuita zvikamu izvo kureba kwacho kunotaridzwa x, y, z, semu. mufananidzo 1. Kubva pakufanana kwemakona matatu anoenderana, tinowana zviyero:

kwatinotsanangura:

Oraz

kwatinotsanangura:

Bvisa mativi ekuenzana akanyorwa neasterisk:

 Kupfupisa mativi ose ne x − z, tinowana - a/b = 1, zvinoreva kuti a + b = 0. Asi nhamba a, b ndiyo kureba kwezvigadziko zvetrapezoid. Kana nhamba yavo iri zero, ivo zvakare zero. Izvi zvinoreva kuti mufananidzo wakafanana ne trapezoid haugone kuvapo! Uye sezvo rectangles, rhombuses uye masikweya ariwo trapezoid, saka, mudiwa Reader, hapana rhombuses, rectangles uye masikweya angave ...

Saizvozvo

Kugovera ruzivo ndiko kunonyanya kunakidza uye kunetsa pazviitwa zvina zvakakosha. Pano, kekutanga, tinosangana nechiitiko chakajairika mukukura: "fungidzira mhinduro, uye tarisa kana iwe wakafungidzira zvakanaka." Izvi zvinonyatso kuratidzwa naDaniel K. Dennett ("Maitiro Ekuita Zvikanganiso?", In It Is - A Scientific Guide to the Universe, CiS, Warsaw, 1997):

Iyi nzira ye "kufungidzira" haikanganisi hupenyu hwedu hwevanhu vakuru - zvichida nokuti tinoidzidza kare uye kufungidzira hakuna kuoma. Ideologically, chiitiko chimwe chete chinoitika, semuenzaniso, mumasvomhu (akazara) induction. Munzvimbo imwe chete, isu "tinofungidzira" fomula tobva tatarisa kuti fungidziro yedu ndeyechokwadi. Vadzidzi vanobvunza nguva dzose kuti: “Takaziva sei muenzaniso wacho? Ringabudiswe sei?" Apo vadzidzi vanondibvunza mubvunzo uyu, ndinoshandura mubvunzo wavo kuva joke: "Ndinoziva izvi nokuti ndiri nyanzvi, nokuti ndinobhadharwa kuziva." Vadzidzi vekuchikoro vanogona kupindurwa nenzira imwe chete, chete zvakanyanya.

Chiitwa. Ziva kuti tinotanga kuwedzera nekunyora kuwandisa nechikamu chepasi, uye kupatsanura nechikamu chepamusoro.

Mubatanidzwa wemazano maviri

Vadzidzisi veMasvomhu vagara vachiratidza kuti chatinodaidza kuti kupatsanurwa kwevanhu vakuru mubatanidzwa wemazano maviri akasiyana: Housing i kuparadzana.

Wekutanga (Housing) inoitika mumabasa uko archetype iri:

Divide-divide Aya mabasa akadai se:

? (Tinochengeta maitiro ekutanga edambudziko iri, akatorwa mubhuku rekushandisa raJulian Zgozalewicz rakaburitswa muKrakow muna 1892 - iyo złoty ndiyo Rhenish złoty, mari yaive ichitenderera muAustro-Hungarian Empire kusvika pakutanga kwezana ramakore rechiXNUMX).

Zvino funga matambudziko maviri ne bhuku rekare remasvomhu muchiPolish, baba Tomasz Clos (1538). Kuparadzana here kana kuti coupe? Zvigadzirise nenzira iyo vana vechikoro muzana ramakore rechi XNUMX vanofanira:

(shandurudzo yechiPolish kuenda kuPolish: Pane quart nemapoto mana mudhiramu. Poto ine maquarts mana. Mumwe akatenga 20 mbiya dzewaini ne50 zł yekutengesa. Mutero uye mutero (excise?) ichava 8 zł. Yakawanda sei kutengesa chikamu kuti uwane 8 zł?)

Mitambo, physics, congruence

Dzimwe nguva mumitambo unofanirwa kugovera chimwe chinhu ne zero (chinangwa chepakati). Zvakanaka, vatongi neimwe nzira vanobata nazvo. Nekudaro, mune abstract algebra ivo vari pachirongwa. non-zero uwandumativi ayo ari zero. Inogona kunyange kutsanangurwa zviri nyore.

Funga nezvebasa F rinobatanidza poindi (y, 0) nenzvimbo iri mundege (x, y). Chii chinonzi F², ndiko kuti, kuurayiwa kweF kaviri? Zero basa - poindi imwe neimwe ine mufananidzo (0,0).

Chekupedzisira, asiri-zero uwandu ane sikweya 0 chinenge chingwa chemazuva ese chenyanzvi dzefizikisi, uye nhamba dzechimiro a + bε, apo ε ≠ 0, asi ε² = 0, masvomhu vanofona nhamba mbiri. Izvo zvinoitika mukuongorora kwemasvomhu uye mukusiyanisa geometry.

Mushure mezvose, pane chimwe chinhu chiri musvomhu chine kupatsanurwa ne zero mune rinenge zita. Inobva kusangana. Rega Z iratidze seti yemanhamba. Kupatsanura seti Z ne p kunoreva kuti tinoenzanisa nhamba imwe neimwe (integer) kune vamwe vamwe, kureva, kune avo mutsauko wavo unopatsanurika. Saka, kana tave nemhando shanu dzenhamba dzinoenderana nenhamba 0, 1, 2, 3, 4 - zvinogoneka zvakasara kana zvapatsanurwa na5. Mushonga wakanyorwa seizvi:

mod kana mutsauko wakawanda.

Pa = 2, tinongova nenhamba mbiri: 0 na 1. Kupatsanura zvikamu zviviri muzvikamu zviviri zvakadai zvakangofanana nekuzvipatsanura kuita zvakaenzana uye zvisinganzwisisike. Ngatichitsivai izvozvi. Musiyano unogara uchipatsanurwa ne1 (chero nhamba inopatsanurwa na1). Zvinoita here kutora =0? Ngatiedzei: kana musiyano wenhamba mbiri uchiwanda zero riini? Chete kana nhamba mbiri idzi dzakaenzana. Saka kupatsanura seti yenhamba ne zero zvine musoro, asi hazvifadze: hapana chinoitika. Zvisinei, zvinofanira kusimbiswa kuti uku hakusi kupatsanurwa kwenhamba mupfungwa inozivikanwa kubva kuchikoro chepuraimari.

Zviito zvakadaro zvinongorambidzwa, pamwe chete nemasvomhu akareba uye akafara.

Mupunga. 2. Kuzivikanwa kwenhamba uchishandisa kuenzanisa

(muti 5 uye muti 2)