Euler umzobo: imizekelo namathuba

IMathematika ngokwesiseko inzululwazi nje, ukuba kude nezimaphambili ezingundoqo. Ngenxa yoko, iperi-apile triple nga ngokwegrafu ebonisa imisebenzi esisiseko ukuba isiseko yemathematika, kodwa kamsinya nje womgca umsebenzi lusanda, ezi zinto akwanelanga. Umntu wazama ukuyichazela kwi apile imisebenzi kwisethi obungapheliyo? Isibakala le nto kukuba akukho. Le ngxuba iingqiqo, leyo isebenza izibalo ekugwebeni yakhe, yingxaki ngakumbi kwabonakala imbonakalo ezibonwayo, nto leyo eya ziyilelwe ukuba kube lula ukuqonda. Noko ke, ulonwabo njengoko abafundi mihla, nenzululwazi ngokubanzi, ziye sirhoxisiwe zilandelayo Euler, imizekelo kunye namathuba apho sixoxe ngezantsi.

A incinane

April 17, 1707 banika ihlabathi inzululwazi Leonarda Eylera - Isazinzulu ebalaseleyo yayo iminikelo kwimathematika, inzululwazi, imikhumbi kunye theory yomculo nemikhuba. imisebenzi yakhe ziyavunywa kwaye ibango kule mini ehlabathini jikelele, nangona inzululwazi na ukuma ngxi. Eyona ezihlekisayo kukuba uMnu Euler yabandakanyeka ngqo kuphuhliso lwesikolo Russian zezibalo ephakamileyo, ngakumbi ke kuba ukuthanda oko, yena kabini wabuyela karhulumente wethu. Le Isazinzulu wayenobuchule elikhethekileyo ukwakha eziselubala algorithms yayo logic, ukusika bonke okungeyomfuneko yaye akukho xesha ihamba ukusuka jikelele ukuya ethile. Asiyi Unalungelo bonke ubuhle bayo, njengoko kuya kuthatha ixesha elininzi, ize makhe sibuyele umxholo wenqaku. Yaba nguye lowo wacebisa ukusetyenziswa lumelo olubonakalayo lwe imisebenzi iiseti. Euler idayagramu nesisombululo na, nkqu imisebenzi enzima kakhulu ilungiswe, nako ukuyichazela abangaboniyo.

Yintoni ngumongo?

Nto ithetha ukuba, Euler zilandelayo kwisazobe oboniswe ngezantsi zingasetyenziswa kuphela kwimathematika, njengoko ingqiqo ka "iiseti" Akubona ukuba ingqeqesho. Ngoko, baye basebenzisa kulawulo ngempumelelo.

Le nkqubo ubonisa ulwalamano ngasentla icwangcisa A (inani ngqiqweni), B (integers kusengqiqweni) kunye C (amanani zendalo). Iizangqa zibonisa ukuba iseti idityanisiwe iseti B, ngoko ke iseti A swi yendlela yokwenza nabo. Umzekelo elula, kodwa uchaza ngokucacileyo nkcukacha ze "iiseti ulwalamano 'ukuba abstract kakhulu uthelekiso ngokwenene xa kuphela ngenxa yokungapheli yabo.

logic algebra

Le ndawo ekuqiqeni kwemathematika isebenza iingxelo, nto leyo ibe zombini ubhalo lokwenyaniso nolobuxoki. Ngokomzekelo, ukususela phawu: inani 625 liyohluleka ngo-25, inani 625 liyohluleka ngo-5, inani 625 ilula. Imvume yokuqala neyesibini - inyaniso, ngeli lixa - ubuxoki. Kakade ke, xa kusenziwa kuba nzima ngakumbi, kodwa ingongoma siboniswa ngokucacileyo. Kakade ke, isigqibo kwakhona inxaxheba Euler umzobo, imizekelo ukusebenzisa kwabo lula kakhulu kwaye ongenantandabuzo ngoyaba.

A bit mbono:

• Makhe iseti A and B zikhona kwaye lilambatha, ngoko ukusebenza kweendlela le ke ngumbutho ezichazwe zilandelayo kuphika.
• Kuhlangana iiseti A no-B iquka izinto ebe zizezakho kwixesha elinye njengoko iseti A bayimisa B.
• Izayamaniso A no-B iquka izinto ebe zizezakho ukuya iseti A okanye B
• A kuphika iseti - iseti entlantlu izinto ezo ndingenguye iseti A.

Konke oku kwakhona uchazwa Euler umzobo ubuhlakani, njengokuba nabo umsebenzi ngamnye, nokuba iqondo ubunzima kuba kuyacaca nebonakalayo.

Elikuwo algebra ekuqiqeni

Ukucinga ukuba 1 no 0 ichazwe kwaye ezikhoyo ezahlukeneyo A, ngoko:

• A kuphika le kuphika iseti luluhlu A;
• A nobuninzi umanyene ne_A 1;
• A nobuninzi womanyano 1 1;
• A komdibaniso iseti kunye ngokwayo luluhlu A;
• Association of A 0 luluhlu A;
• A nobuninzi kwisiphambuka se- ne_A ngu 0;
• A nobuninzi kwisiphambuka se- ngokwayo luluhlu A;
• kuhlangana A 0 ngu 0;
• kuhlangana A 1 iseti A.

Eyona engundoqo iimpawu algebra ekuqiqeni

Vumela iiseti A and B zikhona kwaye lilambatha, ngoko:

• ngokuba kuhlangana kunye yeemanyano iiseti A and B izenzo nomthetho Ihlelo;
• ngokuba kuhlangana kunye yeemanyano iiseti A and B izenzo nomthetho associative;
• ngokuba kuhlangana kunye yeemanyano iiseti A and B izenzo nomthetho ngayinye;
• ukwalela kuhlangana A and B kuhlangana kuphika ka A and B;
• ukwalela komdibaniso iiseti A no-B yeyona manyano lwe kuphika ka A no-B

Ngezantsi ziboniswa alandelayo Euler imizekelo ekudibaneni kwaye edibanisa iiseti A, B na C.

amathuba

Imisebenzi Leonarda Eylera ngokufanelekileyo ingqalelo isiseko imathematika mihla, kodwa ngoku zisetyenziswa ngempumelelo iinkalo zezinto ezenziwa luluntu ukuba lutsha, ukuba ubuncinane ulawulo loshishino: Euler umzobo, imizekelo neetshathi ukuchaza ezisebenza imifuziselo yophuhliso, nokuba uguqulelo Russian okanye Anglo-American .