Euler dhayagiramu. Euler dhayagiramu - mienzaniso iri pfungwa

Leonhard Euler (1707-1783) - akakurumbira Swiss uye Russian yemasvomhu, nhengo St. Petersburg Academy of Sciences, akawanda hwake muna Russia. The inozivikanwa munyika kwemasvomhu pachisara nhamba, mashoko, uye pfungwa anonzi denderedzwa Eulerian (Euler-Venn dhayagiramu) rinoshandiswa kuratidza yezvinoreva pfungwa uye zvinhu zviri seti.

Dzhon Venn (1834-1923) - Chirungu muzivi uye logician, co-munyori Euler-Venn chati.

Zvinowirirana uye sawirirana pfungwa

The rokuti pfungwa inoreva chimiro mafungiro, kufungisisa zvinokosha zviri boka zvakafanana zvinhu. Ivo vanozivikanwa mumwe kana boka mazwi, "mepu nyika", "The Hukuru kvintseptakkord", "Monday" uye vamwe.

In Kana apo vhoriyamu zvinhu pfungwa wose kana zvishoma muridzi kubudikidza Vhoriyamu vamwe, kutaura enderana pfungwa. Kana chinhu bhuku yakajeka pfungwa haagari kutsanangurwa mumwe, tine nzvimbo ine sawirirana pfungwa.

Uyewo, mumwe nomumwe siyana pfungwa ine yakatarwa ayo zvichibvira ukama. zviri kunoenderana nokuda zvinotevera pfungwa:

• Kuzivikanwa (yokuenzana) mavhoriyamu;
• mharadzano (bindepinde) mavhoriyamu;
• kuzviisa pasi (kuzviisa pasi).

For sawirirana:

• kuzviisa pasi (Kufambisa);
• Kusiyana (contraries);
• kupokana (kontradiktornost).

Schematically, ukama huri pakati Dzidziso pfungwa kunogona akasarudzwa kushandisa madenderedzwa ane Euler-Venn.

yokuenzana nomukadzi

Panyaya iyi, pfungwa anoreva chinhu chimwe. Nokudaro, uwandu umboo pfungwa dzakafanana. Somuenzaniso:

A - Sigmund Freud;

In - muvambi psychoanalysis.

kana:

A - pachivara;

B - ane equilateral rectangle;

C - equiangular rhombus.

Kushandiswa kureva zvachose mungashandisa yeChina Euler.

The mharadzano (bindepinde)

muchikwata ichi zvinosanganisira pfungwa kugoverana nevakawanda zvinowanikwa pachinhu panosangana. Ndiko, kuwanda imwe pfungwa iri zvishoma zvaisanganisira mu kutsanangurwa mumwe:

A - Mudzidzisi;

B - music feni.

Sezvinoonekwa pamuenzaniso uyu, bhuku pfungwa bindepinde: vadzidzisi vamwe boka kungava vanoda mumhanzi, ndiEzekieri - pakati mumhanzi mafeni vanogona kuva vamiririri rokudzidzisa. A yakafanana reshiyo uchava nyaya apo pfungwa A anoita Somuenzaniso, "mugari" uye se B - "autodriver".

Kuzviisa (kuzviisa pasi)

Schematically akaratidza sezvo yakasiyana pamwero Euler chati. The ukama pakati pfungwa iyi vanoonekwa ne chokwadi kuti omurume pfungwa (usingashandi vhoriyamu) iri zvakazara chikamu subordinating (vhoriyamu hombe). Panyaya iyi, muranda haarambi vanonetesa pfungwa zvakazara sezvarayirwa.

Somuenzaniso:

A - muti;

B - mupaini.

Pfungwa achava omurume pfungwa A. Sezvo nemipaini zvinoshanda miti, rokuti A inofambidzana subordinating ari muenzaniso uyu, "rokutora" Pfungwa vhoriyamu V.

Kuzviisa pasi (Kufambisa)

Ratio kunoratidza maviri kana kupfuura pfungwa kungoreva luukse asi Kuva sezvamakaropafadzwa wainyatsotaura akagoverana Generic siyana. Somuenzaniso:

A - klarinetti;

In - gitare;

C - gitare;

D - chiridzwa.

Pfungwa A, B, C havana Zvisinei pindana pamusoro mumwe, vose ndezvaJehovha muchikwata zvenziyo (pfungwa D).

Nevakomana (contraries)

Kurwisana ukama pakati Dzidziso Zvichakadaro relatedness mashoko pfungwa zvakafanana genus. Saka imwe pfungwa ane zvimwe zvivako (zvinhu), apo dzavo nedzimwe anoramba kutsiva pakatarisana muchimiro. Nokudaro, tiri kubata antonyms. Somuenzaniso:

A - the pfupi;

B - hofori.

Euler denderedzwa iri pakatarisana ukama pakati okuti rakakamurwa muzvikamu zvitatu, okutanga rinoenderana pfungwa A, wechipiri - pfungwa, uye wechitatu - vamwe pfungwa zvinobvira.

Controversy (kontradiktornost)

Muchiitiko chino, zvose pfungwa dziri pfungwa vakadarovo. Sezvaiitwa yapfuura muenzaniso, rimwe pfungwa anoratidza zvimwe unhu (unhu), ukuwo mumwe akarambazve navo. Zvisinei, kusiyana kune pakatarisana mafungiro, wechipiri, zvakasiyana pfungwa, hakutsivi pfuma akaramba dzimwe nzira. Somuenzaniso:

A - basa rakaoma;

B - nyore basa (non-A).

Achingoratidza yezvinoreva pfungwa iri mhando, kuti Euler denderedzwa iri muzvikamu zviviri - yechitatu, nhume muchiitiko ichi haako. Saka, pfungwa dziri uyewo antonyms. Muchiitiko chino, mumwe wavo (A) zvinova zvakanaka (achibvumirana chero chiratidzo) uye wechipiri (B kana A) - kunaka (vachiramba wakakodzera chiratidzo), "White Paper" - "haisi chena pabepa", "nyika kare" - "vatorwa kare," nezvimwewo ...

Saka, vhoriyamu nhamba pfungwa pachinhu imwe chinokosha hunhu kusarudza Euler madenderedzwa.

Relations pakati unobatsira

Tinofanira kupatsanura pakati okunze uye muzvizhinji cheBhuku inomiririra Euler madenderedzwa. Pfungwa akakweretwa kubva muzvizhinji kuti akarongeka sayenzi ane zvakakwana rwakafara. Mienzaniso pfungwa uye masvomhu kuuratidza sezvo imwe vanochengeta zvinhu. Anoramba pachavo vari zvemamiriro yakatarwa. "A mujenya zvakawanda, ave kumboadya" (Georg Cantor, muvambi yakatarwa yokuti).

Rokuti rinovira kutakurwa netsamba guru A, B, C, D ... nezvimwewo, zvinhu zviri seti - lowercase: .. A, B, C, D ... etc. Mienzaniso yakatarwa anogona vadzidzi iri imwe mukirasi, mabhuku vakamira. uri chaizvo pasherefu (kana Somuenzaniso, zvose mabhuku mune imwe raibhurari), mapeji ari dhayari, kumuromo mudondo glade, uye zvichingodaro. d.

Uyewo, kana imwe yakatarwa harina chero okunze, zvino anonzi zvibereko chiratidzo uye kunoratidza O. Somuenzaniso, imwe muzvizhinji kuti mharadzano pfungwa pamusoro dzakafanana mitsetse, mumwe muzvizhinji kuti zvingaitwa kuti mukana wokuti vanhu vanga X ² = -5.

Kuita matambudziko

Kugadzirisa vakawanda mabasa anoshandiswa nevakawanda Euler chati. Mienzaniso inoratidza pfungwa kukurukurirana pfungwa kwacho kuisa pfungwa. Inoshandisa pfungwa patafura chokwadi. Somuenzaniso, denderedzwa runotaurwa A zita ichokwadi soumambo. Nokudaro, nzvimbo kunze denderedzwa achava nhema. Kuti tizive nzvimbo yacho chati nokuti pfungwa kushanda anofanira vakarangana kumatunhu zvaraireva Euler dhayagiramu umo tsika yayo nokuda okunze A uye B ndezvechokwadi.

Uchishandisa Euler madenderedzwa akawana paupamhi kushanda mumaindasitiri siyana. Somuenzaniso, mumamiriro ezvinhu ane nyanzvi sarudzo. Kana nyaya iri yainetseka kusarudza remangwana basa iri, unogona kutungamirirwa zvinotevera nzira:

W - zvandiri kuita?

D - zvandinowana?

P - pane ndingayananisira mari zvakanaka?

Tinomiririra ichi muchimiro chati: Euler dhayagiramu (mienzaniso kufunga - the mharadzano reshiyo):

The Zvichaguma avo ounyanzvi hwokugadzira kuti chichava mharadzano pakati madenderedzwa matatu.

Penzvimbo rakatevera Euler-Venn ipi muupenyu masvomhu (yakatarwa yokuti) dzemaitirwe kuti mubatanidzwa uye zvivako. Euler dhayagiramu muzvizhinji mufananidzo zvinhu akanyudzwa mukati rectangle inotaridza waifarirwa yakatarwa (U). Panzvimbo madenderedzwa inogonawo kushandiswa nevamwe namahwindo nemifananidzo, asi chaizvoizvo chinoramba zvakafanana. Figures piringisha nemumwe, maererano nemamiriro ezvinhu enyika dambudziko (mu kupfuura zvavo nyaya). Uyewo, kuti mashoko nemifananidzo vanofanira kunzi maererano. Sezvo zvinhu pasi kukurukurwa anogona kuita nemhando pfungwa dziri mukati dzakasiyana mapazi eumambo chati. Anoritsanangura kunogona mumvuri chairo nzvimbo, nokudaro rinoratidza rekuUnited yakatarwa.

With date rinovira zviri bvumidzwa kuita zvinhu kwemasvomhu akavhiyiwa: Kuwedzera (Verenga anoita zvinhu), kubvisa (musiyano), chokuwanziridza (chigadzirwa). Uyezve, nemhaka Euler-Venn chati anogona kuvhiya pamusoro yakatarwa kuenzanisa nokuwanda kwavo constituent okunze, pasingaverengwi navo.