Kungani singahlukani ngoziro?

Abafundi bangase bazibuze ukuthi kungani nginikela i-athikili yonke odabeni olunjalo lwe-banal? Isizathu inani elimangalisayo labafundi (!) abenza umsebenzi ngaphansi kwegama ngokunganaki. Futhi hhayi abafundi kuphela. Kwesinye isikhathi ngiyabamba kanye nothisha. Bazokwazi ukwenzani abafundi bothisha abanjalo ezifundweni zezibalo? Isizathu esisheshayo sokubhala lo mbhalo kwakuyingxoxo nothisha okwahlukaniswa ngoziro kwakungeyona inkinga ...

Ngoziro, yebo, ngaphandle kokuhlupheka lutho nhlobo, ngoba asikho isidingo sokuyisebenzisa ekuphileni kwansuku zonke. Asiyothenga amaqanda ayiziro. “Kunomuntu oyedwa ekamelweni” kuzwakala kungokwemvelo ngandlela thile, futhi “abantu abaziro” kuzwakala njengokwenziwa. Ongoti bolimi bathi iqanda lingaphandle kwesimiso solimi.

Singakwazi ukwenza ngaphandle kukaziro kuma-akhawunti asebhange futhi: sebenzisa nje - njengakwi-thermometer - obomvu nokuluhlaza okwesibhakabhaka ngamavelu amahle namabi (qaphela ukuthi ngezinga lokushisa kungokwemvelo ukusebenzisa okubomvu ngezinombolo eziphozithivu, kanye nama-akhawunti asebhange kungenye indlela, ngoba imali edonswayo kufanele iqalise isexwayiso, ngakho okubomvu kuyanconywa kakhulu).

Ngokufaka u-zero njengenombolo engokwemvelo, sithinta inkinga yokuhlukanisa Izinombolo zekhadinali od ekhaya. Phakathi kuka-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ....

amandla enombolo ayafana nenombolo yendawo lapho emi khona. Uma kungenjalo, isivele iku-0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, .....

Inombolo yamasethi e-singleton iza okwesibili, inani lamasethi anezakhi ezimbili liza okwesithathu, njalo njalo. Kufanele sichaze ukuthi kungani, isibonelo, singazibali izindawo zabasubathi emiqhudelwaneni zisuka nje. Bese kuthi ophume kuqala athole indondo yesiliva (igolide liye kowina indawo kaziro), njalo njalo. Ebholeni lezinyawo kwasetshenziswa inqubo ethi ayifane - angazi noma Abafundi bayazi yini ukuthi elithi "league" lisho ukuthi " ukulandela okuhle kakhulu." ", futhi iligi enguziro ibizwa ngokuthi "iligi enkulu".

Kwesinye isikhathi sizwa ingxabano yokuthi sidinga ukuqala phansi, ngoba ilungele abantu be-IT. Ukuqhubeka nalokhu kucatshangelwa, incazelo yekhilomitha kufanele ishintshwe - kufanele ibe ngu-1024 m, ngoba lokhu kuyinani lamabhayithi ku-kilobyte (ngizobhekisela ehlayeni elaziwa ososayensi bekhompyutha: "Uyini umehluko phakathi komuntu omusha no umfundi wesayensi yekhompyutha kanye nomfundi wesihlanu walesi sikhungo? ukuthi i-kilobyte ingamakhilobhayithi ayi-1000, okokugcina - ukuthi ikhilomitha ngamamitha angu-1024")!

Omunye umbono, okufanele kakade uthathwe ngokungathi sína, yilokhu: sihlala silinganisa kusukela ekuqaleni! Kwanele ukubuka noma yisiphi isikali kumbusi, esikalini sasekhaya, ngisho nasewashi. Njengoba sikala ukusuka kuziro, futhi ukubala kungaqondwa njengesilinganiso esineyunithi engenasici, kufanele sibale sisuka kuziro.

Kuyinto elula, kodwa...

Masishiye ukucabanga okuvamile futhi sibuyele ekuhlukaniseni ngoziro. Le ndaba ilula futhi bekungaba lula ukube bekungeyona ... pho? Ake sicabange futhi sizame. Kungaba yimalini - eyodwa ihlukaniswe ngoziro? Ake sibone: 1/0 = x. Phindaphinda izinhlangothi zombili ngedinominetha yohlangothi lwesobunxele.

Sithola u-1=0. Kukhona okungalungile! Kwenzenjani? Ah qagela! Ukucabanga ukuthi kukhona i-quotient yobunye kanye ne-zero kuholela ekuphikisaneni. Futhi uma umuntu engakwazi ukuhlukaniswa ngoziro, enye inombolo ingakwazi. Uma, Mfundi, uphakamisa amahlombe akho futhi uzibuze ukuthi kungani umbhali (okungukuthi, mina) ebhala ngama-platitudes anjalo, khona-ke ... ngijabule kakhulu!

Ifomula ethi 0/0 = 0 ingase ivikelwe ngesisekelo senkani, kodwa iphikisana nomthetho wokuthi umphumela wokuhlukanisa inombolo ngokwawo ulingana neyodwa. Impela, kodwa zihluke kakhulu izimpawu ezinjengo-0/0, °/° nokunye okunjalo ku-calculus. Azisho noma iyiphi inombolo, kodwa ziyizimpawu ezingokomfanekiso zokulandelana okuthile kwezinhlobo ezithile.

Encwadini yobunjiniyela bukagesi, ngithole ukuqhathanisa okuthakazelisayo: ukuhlukanisa ngoziro kuyingozi njengogesi wamandla aphezulu. Lokhu kuvamile: Umthetho we-Ohm uthi isilinganiso se-voltage ukumelana silingana nesimanje: V = U / R. Uma ukuphikiswa bekuyi-zero, i-current engapheli ye-theoretically izogeleza ku-conductor, ishisa bonke abaqhubi abangenzeka.

Ngake ngabhala inkondlo ngobungozi bokuhlukanisa ngo-zero usuku ngalunye lwesonto. Ngikhumbula ukuthi usuku olubaluleke kakhulu kwakunguLwesine, kodwa kubuhlungu ngawo wonke umsebenzi wami kule ndawo.

Uma uhlukanisa into ngoziro

NgoMsombuluko ekuseni kakhulu

Iviki okusanda kwenzeka

Usuvele wehluleke kabuhlungu.

Lapho ngoLwesibili ntambama

Ufaka u-ziro edinominethini

Ngizokutshela-ke, unephutha

Isazi sezibalo esibi!

Lapho kuqanda, ngokuhlanekezela,

Ufuna ukuhlukana ngoLwesithathu

Uzongena enkingeni enkulu

Unotshani namanzi ekhanda lakho!

UBartek othile wayenathi.

Wayephambana nemithetho.

NgoLwesine, ihlukaniswa ngoziro.

Akasekho phakathi kwethu!

Uma isifiso esiyinqaba sikubamba

Hlukanisa ngoziro ngoLwesihlanu

Ngizokhuluma iqiniso, ngizokhuluma iqiniso:

Isiqalo esibi sale mpelasonto.

Uma kunguziro, ndawana thize ngoMgqibelo

Umhlukanisi kuzoba owakho (hhayi isibindi)

Guqa ngaphansi kothango lwesonto.

Lokhu ukuvuka kwakho.

Ingabe ufuna uziro ngaphansi kwedeshi,

Yenza iholidi ngeSonto

Letha ushoki, ibhodi elimnyama.

Bhala: ayihlukaniseki ngoziro!

Uziro uhlotshaniswa nokungabi nalutho kanye nokungabi nalutho. Ngempela, wafika ezibalweni njengenani, lapho lingezwa kunoma yikuphi, alishintshi: x + 0 = x. Kodwa manje u-zero uvela kwamanye amanani amaningana, ikakhulukazi njengokuthi isikali siqale. Uma ngaphandle kwefasitela kungekho izinga lokushisa elihle noma isithwathwa, khona-ke ... lokhu kungu-zero, akusho ukuthi akukho ukushisa nhlobo. Itshe lesikhumbuzo sezinga elinguziro akulona elabhidlizwa isikhathi eside futhi alikho nje. Ngokuphambene nalokho, kuyinto efana ne-Wawel, i-Eiffel Tower kanye neSifanekiso Senkululeko.

Hhayi-ke, ukubaluleka kukaziro ohlelweni lwezikhundla ngeke kulinganiswe ngokweqile. Uyazi, Mfundi, uBill Gates unoziro abangaki ku-akhawunti yakhe yasebhange? Angazi, kodwa ngingathanda ingxenye. Ngokusobala, uNapoleon Bonaparte waphawula ukuthi abantu bafana namaqanda: bathola incazelo ngesikhundla. Koka-Andrzej Wajda ethi As the Years, As the Days Pass, umdwebi oshisekayo uJerzy uyaqhuma: "UPhilister uthi ziro, nihil, lutho, lutho, nihil, ziro." Kodwa u-zero ungaba muhle: “u-zero deviation from the normal” kusho ukuthi yonke into ihamba kahle, futhi uqhubeke!

Ake sibuyele kwizibalo. Uziro ungangezwa, ususwe futhi uphindaphindwe ngaphandle kokujeziswa. “Ngenyuke ngoziro kilogram,” kusho uManya ku-Anya. “Futhi lokhu kuyathakazelisa, ngoba ngehle isisindo esifanayo,” kuphendula u-Anya. Ngakho-ke masidle ama-ayisikhilimu angu-ziro ayisithupha izikhathi eziyisithupha, ngeke kusilimaze.

Asikwazi ukuhlukanisa ngoziro, kodwa singahlukanisa ngoziro. Ipuleti lamadombolo angama-zero linganikezwa kalula kulabo abalinde ukudla. Uzothola malini umuntu ngamunye?

Uziro akalungile noma unegethivu. Lokhu kanye nenombolo okungekuhleи non-negative. Yenelisa ukungalingani x≥0 kanye no-x≤0. Ukuphikisana "into enhle" akuyona "into engeyinhle", kodwa "into engeyinhle noma elingana noziro". Izazi zezibalo, ngokuphambene nemithetho yolimi, zizohlale zithi into "ilingana no-zero" hhayi "zero." Ukuthethelela lo mkhuba, sinalokhu: uma sifunda ifomula x = 0 "x ilingana noziro" bese kuthi x = 1 sifunda "x ilingana neyodwa", engagwinywa, kodwa kuthiwani ngo "x = 1534267" ? Awukwazi futhi ukwabela inani lenombolo kuhlamvu elingu-0⁰noma ukhuphule uziro emandleni amabi. Ngakolunye uhlangothi, ungakwazi ukuqeda i-zero ngokuthanda kwakho... futhi umphumela uzohlala unguziro. 

Umsebenzi womchazi y = a^x, isisekelo esihle sika-a, asilokothi sibe uziro. Lokhu kulandela ukuthi ayikho i-logarithm enguziro. Ngempela, i-logarithm ye-a to base b iyi-eksponenti okufanele isisekelo siphakanyiswe ukuze kutholwe i-logarithm ka-a. Ku-= 0, asikho inkomba enjalo, futhi uziro akanakuba yisisekelo selogarithm. Nokho, u-ziro “edenominayitha” yophawu lukaNewton ungokunye. Sicabanga ukuthi lezi zingqungquthela aziholeli ekuphikiseni.

ubufakazi bamanga

Ukuhlukaniswa ngoziro kuyisihloko esivamile sobufakazi obungamanga, futhi kwenzeka ngisho nakochwepheshe bezibalo abanolwazi. Ake ngikunike izibonelo ezimbili engizikhonzile. Eyokuqala i-algebraic. "Ngizofakazela" ukuthi zonke izinombolo ziyalingana. Ake sithi kunezinombolo ezimbili ezingalingani. Ngakho-ke, omunye wabo mkhulu kunomunye, ake a > b. Ake sicabange ukuthi u-c umehluko wabo

c \uXNUMXd a -b. Ngakho sino - b = c, lapho a = b + c.

Siphindaphinda zombili izingxenye zokugcina ngo-a - b:

a² – ab = ab + ac – b2 – bc.

Ngihumusha elithi ak ngiyisa kwesokunxele, vele ngikhumbula ngokushintsha uphawu:

a² - ab - ac = ab - b2 - bc.

Angibandakanyi izici ezijwayelekile:

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

Ngiyabelana futhi nginakho engangikufuna:

a = b.

Futhi empeleni ngisho nomfokazi, ngoba ngangicabanga ukuthi a > b, futhi ngathola ukuthi a = b. Uma esibonelweni esingenhla "ukukopela" kulula ukuqaphela, khona-ke ebufakazini bejometri ngezansi akulula kangako. Ngizofakazela ukuthi ... i-trapezoid ayikho. Isibalo esivame ukubizwa nge-trapezoid asikho.

Kodwa ake sithi okokuqala kukhona into efana ne-trapezoid (ABCD esithombeni esingezansi). Inezinhlangothi ezimbili ezifanayo ("izisekelo"). Ake selule lezi zisekelo, njengoba kuboniswe esithombeni, ukuze sithole ipharalelogramu. I-diagonal yayo ihlukanisa enye idayagonali ye-trapezoid ibe amasegimenti ubude bawo buchazwa ngokuthi x, y, z, njengaku. umfanekiso 1. Kusukela ekufananeni konxantathu abahambisanayo, sithola izilinganiso:

lapho sichaza khona:

Oraz

lapho sichaza khona:

Susa izinhlangothi zokulingana ezimakwe ngezinkanyezi:

 Ukufinyeza izinhlangothi zombili ngo x − z, sithola – a/b = 1, okusho ukuthi a + b = 0. Kodwa izinombolo a, b ubude bezisekelo ze-trapezoid. Uma isamba sawo singuziro, kusho ukuthi nawo anguziro. Lokhu kusho ukuthi isibalo esifana ne-trapezoid asikwazi ukuba khona! Futhi njengoba ama-rectangles, ama-rhombuses nezikwele nazo ziyi-trapezoid, ngakho-ke, Mfundi othandekayo, awekho ama-rhombuses, ama-rectangles nezikwele noma ...

Qagela Qagela

Ukwabelana ngolwazi kuyinselele kakhulu futhi kuyinselele emisebenzini emine eyisisekelo. Lapha, ngokokuqala ngqa, sihlangabezana nesenzakalo esivame kakhulu ebudaleni: "qagela impendulo, bese uhlola ukuthi uqagele kahle." Lokhu kuvezwe kahle kakhulu nguDaniel K. Dennett (“Indlela Yokwenza Amaphutha?”, kwethi How It Is – A Scientific Guide to the Universe, CiS, Warsaw, 1997):

Le ndlela "yokuqagela" ayiphazamisi impilo yethu yabantu abadala - mhlawumbe ngoba siyifunda kusenesikhathi futhi ukuqagela akunzima. Ngokwemibono, kwenzeka okufanayo, isibonelo, ekungenisweni kwezibalo (okuphelele). Endaweni efanayo, "siqagela" ifomula bese sihlola ukuthi ukuqagela kwethu kulungile yini. Abafundi bahlale bebuza: “Sazi kanjani iphethini? Ingakhishwa kanjani?" Lapho abafundi bengibuza lo mbuzo, ngiphendula umbuzo wabo ube yihlaya: "Ngiyazi lokhu ngoba nginguchwepheshe, ngoba ngikhokhelwa ukwazi." Abafundi esikoleni bangaphendulwa ngesitayela esifanayo, kuphela ngokujulile.

Ukuzivocavoca. Qaphela ukuthi siqala ukuhlanganisa nokubhala ukuphindaphinda ngeyunithi ephansi kakhulu, nokuhlukanisa ngeyunithi ephezulu kakhulu.

Inhlanganisela yemibono emibili

Othisha bezibalo bebelokhu beveza ukuthi lokhu esikubiza ngokuhlukana kwabantu abadala ukuhlangana kwemibono emibili ehlukene ngokwengqondo: Izindlu i ukwehlukana.

Eyokuqala (Izindlu) kwenzeka emisebenzini lapho i-archetype iyi:

Hlukanisa-hlukanisa Lena imisebenzi efana nale:

? (Sigcina isitayela sangempela sale nkinga, esithathwe encwadini yesandla kaJulian Zgozalewicz eyanyatheliswa e-Krakow ngo-1892 - i-złoty yi-Rhenish złoty, imali eyayisatshalaliswa eMbusweni wase-Austro-Hungary kuze kube sekuqaleni kwekhulu lesi-XNUMX).

Manje cabanga ngezinkinga ezimbili incwadi yezibalo endala kakhulu ngesi-Polish, ubaba uTomasz Clos (1538). Ingabe i-division noma i-coupe? Ixazulule ngendlela izingane zesikole zekhulu lesi-XNUMX okufanele:

(Ukuhunyushwa kwesiPolish kuya kusiPolishi: Kukhona ilitha namabhodwe amane emgqonyeni. Ibhodwe lingamalitha amane. Omunye uthenge imiphongolo yewayini engama-20 ngo-50 zł wokuhweba. Inkokhelo nentela (impahla?) izoba ngu-8 zł. Malini uthengise ikota ukuze uthole u-8 zł?)

Ezemidlalo, i-physics, i-congruence

Kwesinye isikhathi kwezemidlalo kumele uhlukanise okuthile ngoziro (isilinganiso somgomo). Nokho, amajaji ngandlela thize abhekana nakho. Nokho, ku-algebra abstract baku-ajenda. amanani angewona aziroisikwele sakhe singuziro. Kungachazwa kalula.

Cabangela umsebenzi F ohlobanisa iphuzu (y, 0) nephuzu endizeni (x, y). Yini i-F², okungukuthi, ukubulawa kabili kwe-F? Umsebenzi onguziro - iphuzu ngalinye linesithombe (0,0).

Okokugcina, amanani angewona aziro ayisikwele sawo esingu-0 cishe ayisinkwa sansuku zonke sezazi zefiziksi, nezinombolo zefomu elithi a + bε, lapho ε ≠ 0, kodwa ε² = 0, izazi zezibalo ziyabiza izinombolo eziphindwe kabili. Zenzeka ekuhlaziyweni kwezibalo naku-geometry ehlukile.

Phela kunento ethile kwi-arithmetic ehlukanisa ngoziro okungenani egameni. Ivela ukuhlangana. Vumela u-Z asho isethi yamanani aphelele. Ukwehlukanisa isethi Z ngo-p kusho ukuthi silinganisa inombolo ngayinye (inamba) kwabanye, okungukuthi, kulawo umehluko wabo ohlukaniswa ngawo. Ngakho-ke, uma sinezinhlobo ezinhlanu zezinombolo ezihambisana nezinombolo 0, 1, 2, 3, 4 - izinsalela ezingenzeka uma zihlukaniswa ngo-5. Ifomula ibhalwe kanje:

mod lapho umehluko uyi-multiple.

Ku-= 2, sinezinombolo ezimbili kuphela: u-0 kanye no-1. Ukwehlukanisa izinombolo eziphelele zibe amakilasi anjalo kulingana nokuwahlukanisa abe ngokulinganayo futhi abe yinqaba. Masiyishintshe manje. Umehluko uhlale uhlukaniswa ngo-1 (noma iyiphi inombolo ephelele ihlukaniswa ngo-1). Kungenzeka yini ukuthatha =0? Ake sizame: nini umehluko wezinombolo ezimbili ukuphindwaphindwa kukaziro? Kuphela uma lezi zinombolo ezimbili zilingana. Ngakho-ke ukuhlukanisa iqoqo lezinombolo ngoziro kunengqondo, kodwa akujabulisi: akukho okwenzekayo. Kodwa-ke, kufanele kugcizelelwe ukuthi lokhu akukhona ukuhlukaniswa kwezinombolo ngomqondo owaziwa kusukela esikoleni samabanga aphansi.

Izenzo ezinjalo zivinjelwe nje, kanye nezibalo ezinde nezibanzi.

Ilayisi. 2. Ukuhlonza izinombolo kusetshenziswa ukuqhathanisa

(imodi 5 kanye nemodi 2)