Euler idayagramu. Euler umdwebo - izibonelo ubuhlakani

Leonhard Euler (1707-1783) - sezibalo esidumile Swiss kanye isiRashiya, ilungu Petersburg Academy of Sciences, ingxenye enkulu yokuphila kwakhe e-Russia. Ezaziwa kakhulu e- izingabunjalo, izibalo, ulwazi, kanye logic kubhekwa umbuthano Eulerian (Euler-umdwebo) isetshenziselwe abonisa kwenkululeko imiqondo netakhiwo lishona.

Dzhon Venn (1834-1923) - Isazi sefilosofi esiyiNgisi futhi logician, co-umbhali we Euler-Venn imidvwebo.

imiqondo ehambisanayo futhi engahambisani

Umqondo gama lisho uhlobo ukucabanga, khomba izici ezibalulekile nekilasi izinto ezifanayo. Bona ngokuthandana eyodwa noma iqembu amazwi, "nebalazwe", "I kvintseptakkord evelele", "uMsombuluko", nabanye.

Esimeni lapho izakhi ivolumu umqondo ngokuphelele noma ingxenye okungewakho ivolumu nezinye, ukhuluma ngani imiqondo ehambisanayo. Uma kunoma iyiphi ingxenye ivolumu kuchazwe umqondo ingeyona kwenkululeko nezinye, siba indawo imiqondo engahambelani.

Ngakwelinye ihlangothi, ngayinye izinhlobo imiqondo has awayo ubudlelwano kungenzeka. ke luhambisana for imiqondo elandelako:

• ungubani (kwefrakshini) amavolumu;
• empambana (ukugqagqana) amavolumu;
• kwakuwukuthi (kwakuwukuthi).

Ukuze akuhambisani:

• kwakuwukuthi (ukubambisana);
• Ngokuphambene (contraries);
• ukungqubuzana (kontradiktornost).

Schematically, ubudlelwane phakathi imiqondo logic kungenziwa oqokiwe usebenzisa nemibuthano Euler-Venn.

ubudlelwane kwefrakshini

Kulokhu, umqondo, atjho into efanako. Ngakho, inani imiqondo idatha ziyafana. Ngokwesibonelo:

A - Freud sasho;

Ngo - umsunguli psychoanalysis.

noma:

A - sikwele;

B - i isikwele equilateral;

C - rhombus equiangular.

Ukusetshenziswa lapho kubhekiselwe othandweni imibuthano ezifanayo ngokuphelele Euler.

Empambana (ukugqagqana)

Lesi sigaba sihlanganisa nomqondo ukwabelana izakhi ezivamile wathola maqondana zemigwaqo. Okungukuthi, inani omunye imiqondo kancane kufakwe kwenkululeko kwenye:

A - umfundzisi;

B - elibonisa abathandi bomculo.

Njengoba ungase ubone kulolu Ngokwesibonelo, ivolumu imiqondo kuyendlulela: othisha iqembu ethile kungase kube abathandi bomculo, futhi kungokufanayo nangendoda - phakathi bomculo kungaba abameleli yokufundisa umsebenzi. A isilinganiso esifanayo kuyoba esimweni lapho umqondo A wenza, isibonelo, "isakhamuzi" futhi njengoba B - "autodriver".

Ukuhanjiswa (kwakuwukuthi)

Schematically wabonisa njengoba isikali ehlukene Euler idayagramu. Ubudlelwane phakathi imiqondo kulokhu zinezikhathi yokuthi umqondo okhonzile (ivolumu sakugcina) is fully ingxenye subordinating (umthamo ngaphezulu). Kulokhu, lo inceku ayikwazi ucede umqondo ihambisana ngokugcwele.

Ngokwesibonelo:

A - esihlahleni;

B - zikaphayini.

Umqondo kuyoba ilawulwe A. umqondo Njengoba zikaphayini osebenza ku izihlahla, A eside kuba subordinating kulesi sibonelo, "iyavuleka" umqondo ivolumu V

Be (ukubambisana)

Lokubiza likhombisa imiqondo emibili noma ngaphezulu alizimele, kodwa okuqondene lapho esibekiwe wabelane ububanzi ejwayelekile. Ngokwesibonelo:

A - negekle;

Ngo - isiginci;

C - violin;

D - insimbi yomculo.

Umqondo A, B, C kungukuthi Nokho agqagqene maqondana nomunye, zozela zonke, basonta isigaba zezinsimbi zomculo (umqondo D).

Okuphambene (contraries)

Ukumelana ubudlelwano phakathi imiqondo kusho imiqondo idatha relatedness ukuba uhlobo lwe efanayo. Ngakho omunye imiqondo anezakhi ezithile (izici), ngenkathi ezinye zazo ophika esikhundleni obuhlukile uhlamvu. Ngakho, sibhekene nabomcondvophika. Ngokwesibonelo:

A - the yemifino;

B - giant.

Euler umbuthano ngesikhathi ubuhlobo okuphambene phakathi imigomo ihlukaniswe izingxenye ezintathu, olokuqala okuhambelana umqondo A, kwesibili - umqondo, futhi eyesithathu - lonke imiqondo kungenzeka.

Impikiswano (kontradiktornost)

Kulokhu, kokubili imiqondo imibono of fana hlobo. Njengoba kulesibonelo langaphambilini, omunye imiqondo kubonisa izimfanelo ezithile (izimfanelo), kuyilapho ezinye waphika kubo. Nokho, ngokungafani kuya sengqondo okuphambene, wesibili, umbono okuphambene, akusho ukuthi akufanele kusetshenziswe impahla inqatshelwe enye. Ngokwesibonelo:

A - onzima;

B - umsebenzi elula (non-A).

Iveza kwenkululeko imiqondo yalolu hlobo, indingilizi Euler ihlukaniswe yaba izingxenye ezimbili - yesithathu, umlamuli kulokhu ayikho. Ngakho, imiqondo yamagama futhi bomcondvophika. Kulokhu, omunye wabo (A) iba omuhle (ekuvumeleni okubonisa) kanti eyesibili (B noma A) - ezimbi (bephika uphawu olufanele), "I-White Paper" - "akuyona iphepha elimhlophe", "umlando kazwelonke" - "umlando abangaziwayo," etc ...

Ngakho, ivolumu isilinganiso imiqondo maqondana nomunye kuwuphawu ukhiye sokunquma Euler imibuthano.

Ubudlelwano phakathi amasethi

Kufanele futhi ukuhlukanisa emkhatsini wetincenye teluhlaka kanye sebuningini ivolumu amelela Euler imibuthano. Umqondo lathathwa sebuningini isayensi zezibalo futhi ezibanzi ngokwanele. Izibonelo logic nezibalo njenge isethi ethile yezinto. Objects ngokwabo izakhi isethi. "Kuningi Ziningi, njengoba icatshangwe" (Georg Cantor, umsunguli isethi theory).

Isikhundla amasethi eyenziwa ngu ofeleba A, B, C, D ... njll, izakhi amasethi - ezincane: .. A, b, c, d ... njll Izibonelo isethi kungenzeka abafundi elise ekilasini afanayo, amabhuku ezinombolo emi. eshalofini ethize (noma, isibonelo, zonke izincwadi emtatsheni esithile), amakhasi e ngedayari, amajikijolo endaweni esobala enokukhanya kwelanga ihlathi, nokunye. d.

Ngakwelinye ihlangothi, uma isethi ethile ayinazo izakhi, khona-ke kubizwa ngokuthi uphawu ingenalutho futhi abonisa Ø. Ngokwesibonelo, sebuningini empambana amaphuzu lemigqa okufanayo, sebuningini izixazululo ezothando x ² = -5.

Ukuhlangabezana izinselele

Ukuxazulula inani elikhulu imisebenzi kabanzi Euler idayagramu. Izibonelo khombisa logic of zokuxhumana logic imisebenzi setha theory. Isebenzisa imiqondo kwethebula iqiniso. Ngokwesibonelo, indingilizi ezikhonjiswe Yigama isizinda iqiniso. Ngakho, leyo ndawo ngaphandle umbuthano kuyoba amanga. Ukuze sithole indawo yeshadi for ukusebenza logic kufanele achanyuselwa izifunda ngokuchaza Euler umdwebo lapho izindinganiso zalo walezinto A no B ziyiqiniso.

Ukusebenzisa Euler imibuthano etholakele isicelo ebanzi esisebenzayo kulezo zimboni. Ngokwesibonelo, esimweni sikhethe okhokhelwayo. Uma isihloko ikhathazekile mayelana nokukhetha umsebenzi esikhathini esizayo, kungase uholwe nenqubo elandelayo:

W - lokho Ngithanda ukwenza?

D - ukuthi ngithola?

P - kunami ungenza imali ezinhle?

Simelela lokhu ngesimo imidvwebo: Euler umdwebo (izibonelo ubuhlakani - isilinganiso empambana):

Umphumela walokhu uyoba labo ubuchwepheshe ukuthi kuyoba empambana emibuthano ezintathu.

indawo Hlukanisa elandelayo Euler-Venn hlala kwi-mathematics (isethi theory) kulesi sibalo inhlanganisela kanye izakhiwo. Euler umdwebo sebuningini izakhi isithombe ebiyelwe konxantathu ekhombisa isethi jikelele (U). Esikhundleni imibuthano lungasetshenziswa nezinye izibalo evaliwe, kodwa ngokuyisisekelo ayiguquki. Izinombolo aphambana nomunye, ngokuvumelana nemibandela inkinga (esimweni jikelele kakhulu). Futhi, izibalo idatha kufanele ifakwe ilebuli efanele. Njengoba izakhi olucutshungulwayo bangase benze amasethi amaphuzu kubekwe phakathi izingxenye ezahlukene yombonisomdwebo. Kususelwa it can umthunzi endaweni ethize, kanjalo zimise isethi elalisanda kumiswa.

Nge amasethi wedatha kwamukelekile ukwenza eziyisisekelo imisebenzi zezibalo: kwalokho (isamba amasethi izakhi), ukususa (umehluko), ukubuyabuyelela (umkhiqizo). Ngaphezu kwalokho, sibonga Euler-Venn imidvwebo ongenza imisebenzi kwi ukuqhathanisa isethi nesibalo izakhi zabo abalekeleli singabali kubo.