Hēura hoahoa: tauira me ngā whai wāhitanga

Ko te tino Pāngarau he pūtaiao waitara, ki te neke atu koutou i te ariā taketake. Ko te kupu, he rua o te aporo takitoru e taea kauwhata whakaatu i te ngā mahi taketake e te hunga i te pūtake o te pāngarau, engari, no te te waka rererangi o mahi whakawhānui, e kore he nui enei taonga. tamata tētahi ki te whakaatu i runga i te aporo ngā mahi i runga i huinga mure ore? Ko te meka o te mea he e kore. Ko te atu matatini te ariā, i whakahaere te pāngarau i roto i tona whakawa, te raruraru atu whakaaro reira ratou faaiteraa ataata, e pai hangaia kia ki hāpai i te māramatanga. Heoi, i roto i te oaoa rite ngā ākonga hou, me te pūtaiao i roto i te whānui, kua mawehe atu e whai ake nei Hēura, tauira me ngā whai wāhitanga e aparau i tatou i raro.

He hītori iti

April 17, 1707 hoatu te ao te pūtaiao Leonarda Eylera - kaiputaiao tino nei takoha ki te pāngarau, te ahupūngao, te pahi, me te ara ariā waiata e kore e piriponotanga. E mohio ana mahi, me te i roto i te tono ki tenei ra huri noa te ao, ahakoa te meka e kore e pūtaiao tu tonu. Ngā whakangahau Ko te meka i whai wāhi tika Mr. Hēura i te whanaketanga o te kura Russian o pāngarau teitei, te atu pera no te i pai ai o whakarau, ia rua hoki ki to tatou ahua. i te pūtaiao he kaha ahurei ki te hanga mārama i roto i ona hātepe arorau, tapahia ana tikanga katoa, me te i roto i kore wa neke i te whānui ki te tauwhāiti. E kore matou e rarangitia ona hua katoa, rite ka tangohia e te reira i te nui o te wā, ka kia tatou hoki ki te kaupapa o te tuhinga. Ko ia te tangata e te whakaaro te whakamahi o te kanohi whakairoiro o ngā mahi i runga i ngā huinga. Hēura otinga hoahoa ki tetahi, ara nga mahi uaua tino rite, taea ki te whakaatu ngā.

He aha te mea te faufaa?

I roto i te mahi, te Hēura whai taea te whakamahi hoahoa o whakaaturia nei te i raro nei e kore anake i roto i te pāngarau, kia rite ki te ariā o "huinga" e kore e ahurei ki te ako. Na, kua ratou kua pai tono i roto i te whakahaere.

E whakaatu ana te kaupapa whakatakoto ana te hononga i runga ake te (te tokomaha noatia), B (tau tōpu kouma) me C (tau tūturu). Porowhita tohu e ngā te huinga e i roto i te huinga i te B, ka kore e whakaritea te A whakawhiti ki a ratou. He tauira o te kuware, engari mārama whakamārama te pau o "huinga hononga" e he waitara rawa hoki te whakarite tūturu ki te anake te mea o ratou mutu-.

taurangi arorau

Tenei rohe o arorau pāngarau mahi tauākī, e taea e rua huru pono, me te teka. Hei tauira, i te timatanga: te tau 625, ko te wehewehe i te 25, te tau 625, ko te wehewehe i te 5, te tau 625, ko te ohie. Ko te whakaae tuatahi, me te tuarua - te pono, i te muri - he teka. O te akoranga, i roto i te mahi he reira uaua ake, engari whakaaturia te wāhi kei te mārama. A, o te akoranga, whai wāhi ano te whakatau hoahoa Hēura, tauira o ratou whakamahinga he watea rawa me te pūmanawa ki te tau'a ore ia ratou.

He bit o ariā:

• Kia te A whakaritea, me te B te tīariari, me he kau kahore, ka ko te rōpū e whai ake nei tautuhi me te whakakorehanga mo te mahi whakawhitinga.
• Pūtahitanga o ngā huinga A me B ngā o ngā āhuatanga e no ki te wa taua rite huinga te A me te whakatakotoria B.
• Ngā o A me B ngā o ngā āhuatanga e no ki huinga te A ranei whakatakotoria B.
• He whakakorehanga o te huinga - he huinga e ngā o ngā huānga e kore e nei no ki huinga te A.

Kei te tuhituhi ano tenei katoa rite Hēura hoahoa i roto i arorau, rite tahi ratou ia mahi, ahakoa o te tohu o te uaua riro kitea, me te kitea.

Axioms o taurangi o arorau

Me kī e 1 me 0 e tautuhi me te tīariari i roto i te momo o te, ka:

• He whakakorehanga o te whakakorehanga o te huinga, ko te huinga o A;
• He plurality o roto ki ne_A he 1;
• He plurality o uniana 1 Ko 1;
• He uniana o te huinga ki ake he huinga te A;
• Association o te 0 ko huinga te A;
• He plurality o pūtahitanga ki ne_A ko 0;
• He plurality o te pūtahitanga ki ake he huinga te A;
• pūtahitanga o te 0 ko te 0;
• pūtahitanga o te 1 he huinga A.

Ko te āhuatanga matua o te taurangi o arorau

Kia te A huinga me te B te tīariari, me he kahore kau, ka:

• hoki pūtahitanga me te uniana o huinga A me B mahi ture āpiti;
• hoki pūtahitanga me te uniana o huinga A me B mahi ture herekore;
• hoki pūtahitanga me te uniana o huinga A me B mahi ture tohatoha;
• whakakāhoretanga o te pūtahitanga o te ko B ko te whakawhitinga o negations o te me te B;
• whakakāhoretanga o te uniana o huinga A me B ko te uniana o negations o A me B.

Kei raro e whakaaturia e whai ake tauira whakawhitinga Hēura me te whakakotahi i te huinga A, B me C.

opuaraa

Ko te mahi Leonarda Eylera tika whakaaro te pūtake o te pāngarau hou, engari inaianei e pai te whakamahia ratou i roto i nga wāhi o te mahi a te tangata e he āhua hou, ki te tango i te kāwanatanga rangatōpū i te iti rawa: Hēura hoahoa, tauira, me ngā tūtohi whakaahua nga tikanga o tauira whanaketanga, ahakoa putanga Russian ranei Anglo-American .