Hēura hoahoa. Hēura hoahoa - tauira i roto i te arorau

Leonhard Hēura (1707-1783) - rongonui mathematician Swiss me Russian, he mema o te St Petersburg Academy o Sciences, te nuinga o tona ora i roto i Russia. Ko te-mohiotia pai i roto i te tātari pāngarau, tatauranga, ngā mōhiohio, me whakaaro te arorau te porowhita Eulerian (Hēura-Venn hoahoa) whakamahia ki te tohu i te hōkai o te ariā me ngā āhuatanga o te huinga.

Dzhon Venn (1834-1923) - philosopho Ingarihi me te tangata tohe, tahi-kaituhi o te hoahoa Hēura-huinga.

ariā Hototahi me hotokore

E pā ana te arorau wā ki te ahua o te whakaaro, e whakaata ana i te āhuatanga faufaa o te piha haapiiraa o ngā tūemi ōrite. E tāutuhia ana ratou e tetahi he rōpū o kupu, "mahere ao", "Ko te kvintseptakkord Ngoi", "Rāhina", me ētahi atu ranei.

I roto i te take i reira nga mea timatanga rōrahi o te ariā o whakapau ki wāhanga ranei puritia e te rōrahi o te tahi atu, korero e pā ana ki ngā ariā hototahi. Ki te kore e tetahi huānga o te rōrahi tautuhia ariā no ki te hōkai o te tahi atu, to tatou he wahi ki te ariā hotokore.

I roto i te tahuri, i ia o nga momo o ngā ariā kua ona huinga ake o te whanaungatanga taea. Ko reira hototahi mo te ariā e whai ake nei:

• tuakiri (ōritenga) pukapuka;
• pūtahitanga (inaki) pukapuka;
• subordination (subordination).

Hoki hotokore:

• subordination (ruruku);
• rerekē (contraries);
• totohe (kontradiktornost).

Schematically, e taea te whakaritea te hononga i waenganui i te ariā o arorau mā te whakamahi i te porowhita o Hēura-Huinga.

whanaunga ōrite

I roto i tenei take, te ariā o te tikanga o te mea kotahi. Nä, ko te nui o ngā ariā raraunga ko te taua. Hei tauira:

A - Sigmund Freud;

I roto i - te kaiwhakarewa o psychoanalysis.

rānei:

A - tapawha;

B - he tapawhā equilateral;

C - whakarara rite equiangular.

Whakamahia ki te kōrero ki porowhita tino ōrite Hēura.

Ko te pūtahitanga (inaki)

Tenei kāwai ngā te ariā o te faaiteraa i ngā huānga noa kitea i roto i te pā ana ki pekanga. Ko, te nui o tetahi o nga ariā kei te wāhanga ngā i roto i te hōkai o tetahi:

A - te kaiako;

B - tahi waiata.

Ka rite ki kite i tenei tauira te rōrahi o ngā ariā, īnaki: kia kia etahi rōpū kaiwhakaako i aroha waiata, me te hurihia - i roto i te pā waiata e taea e ngā māngai o te tikanga whakaako. ka waiho te ōwehenga rite i roto i te take i reira he ariā A mahi, hei tauira, "tangata", me te rite B - "autodriver".

Tāpaetanga (subordination)

Schematically tohua rite tauine rerekē Hēura hoahoa. Ko te hononga i waenganui i te ariā i roto i tenei take e āhuatanga e te meka e te ariā kaimahi (iti rōrahi) he tino wāhanga o te ngohengohe (rōrahi nui). I roto i tenei take, e kore e te pononga ruha te ariā tino ū.

Hei tauira:

A - rakau;

B - pine.

Ka kia ngohengohe te ariā ki te ariā A. Mai pā paina ki rakau, te te wā e tau ana ngohengohe i roto i tenei tauira, "ngongo" V. rōrahi ariā

Subordination (ruruku)

tohu Ratio te ariā e rua, neke atu rānei tāuke, engari no te tohua ngā ai ngā kano. Hei tauira:

A - pūtahoro;

I roto i te - guitar;

C - wairingi;

D - he taonga puoro.

E kore e te ariā o te, B, C inaki ki te faatura ki tahi i te tahi, Heoi, no ratou katoa ki te kāwai o waiata (te ariā D).

Ko te ritenga (contraries)

Ātete hononga i waenganui i te ariā o ngā ariā raraunga relatedness toharite ki te puninga kotahi. Ko te kupu e tetahi o nga ariā etahi āhuatanga (āhuatanga), i to ratou atu whakakahore whakakapi ritenga i roto i te huru. Ko te kupu, Kei te mahi tatou ki te kupu tauaro. Hei tauira:

A - ko te papaka;

B - Rapa.

Kei te wehea Hēura porohita i te hononga ritenga i waenganui i nga ngā ki toru wāhanga, ko te tuatahi o e hāngai ki te ariā A, te tuarua - i roto i te ariā, me te tuatoru - te ariā ka taea era atu.

Totohe (kontradiktornost)

I roto i tenei take, ariā e rua he whakaaro o te ahua taua. Ka rite ki i roto i te tauira o mua, tohu tetahi o nga ariā etahi huru maitatai (huru), i te tahi atu whakakahore ratou. Heoi, i roto i te rerekē ki te huru ritenga, te tuarua, te ariā ritenga, e kore te whakakapinga mō taonga whakakahore atu kē. Hei tauira:

A - he mahi uaua;

B - mahi ohie (A-kore).

Te faaite i te hōkai o te ariā o tenei ahua, kua wehea te porohita Hēura kia rua nga wahi - e kore e he tuatoru, takawaenga i roto i tenei take te tīariari. Ko te kupu, Ko nga kupu tauaro hoki nga ariā. I roto i tenei take, tetahi o ratou (A) riro pai (whakaae tetahi tohu) me te tuarua (B A ranei) - tōraro (whakakahore i te tohu e tika ana), "Pepa White" - "E kore te mea he pepa ma", "hītori motu" - "hītori ke," etc ...

Ko te kupu, ko te ōwehenga rōrahi o ngā ariā i roto i te pā ana ki tahi i te tahi, ko te āhuatanga matua whakatau Hēura porowhita.

Whanaungatanga i waenga i ngā huinga

kia wehewehe ano tatou ki waenganui i te huānga me te plurality o rōrahi e tohu Hēura porowhita. Ko te ariā tono i te plurality o pūtaiao pāngarau, me te kua he whanui makona. Tauira o te arorau me pāngarau whakaatu reira rite te huinga etahi o ngā. Ahanoa he āhuatanga o te huinga ratou. "He rota i te rota, kia rite ki te conceivable" (Georg Cantor, te kaiwhakarewa o huinga ariā).

huinga ti'araa kawea e reta whakapaipai A, B, C, D ... etc, āhuatanga o te huinga - pūriki: .. A, b, c, d ... etc. tauira o te huinga kia ākonga kei roto i te akomanga kotahi, pukapuka e tu ana kia. i runga i te papa motuhake (ranei, mo te tauira, nga pukapuka katoa i roto i te whare pukapuka ngā), te mau api i roto i te rātaka, hua i roto i te Ahaaha ngahere, a na i runga i. d.

I roto i te tahuri, ki te kahore tetahi huinga e roto i tetahi huānga, ka huaina a reira ko te tohu pātea, me te tohu o. Hei tauira, he plurality o ngā whakawhitinga o te rārangi whakarara, he plurality o rongoā ki te whārite x ² = -5.

Hui nga wero

Hei whakaoti i te maha nui o ngā mahi e whakamahia whānuitia Hēura hoahoa. Tauira whakaatu te arorau o te kōrero ngā mahi arorau whakaturia ariā. whakamahi te reira i te ariā o te pono tepu. Hei tauira, denoted te porowhita ko te ingoa he rohe pono. Ko te kupu, ko te rohe i waho i te porohita ka waiho he teka. Hei whakatau i te rohe o te tūtohi mo te mahi arorau kia paopao rohe tautuhi Hēura hoahoa i roto i nei e pono ona uara mo te he huānga me B.

kitea Mā te porowhita Hēura whānui tono mahi i roto i ngā ahumahi. Hei tauira, i roto i te āhuatanga ki te whiriwhiri ngaio. Ki te āwangawanga te tumu parau e pā ana ki te kōwhiri i te tikanga a muri, e taea te ārahi i te reira e te paearu e whai ake:

W - he aha ahau rite ki te mahi?

D - e whiwhi ahau?

P - atu i taea te hanga e ahau te moni pai?

tohu tatou i tenei i roto i te puka o ngā hoahoa: Hēura hoahoa (tauira i roto i te arorau - te ōwehenga whakawhitinga):

Ko te hua ka waiho te hunga ngaio e ka waiho i te pūtahitanga o te porowhita e toru.

wahi motuhake e whai ake nei Hēura-Venn noho i roto i te pāngarau (huinga ariā) i roto i te tātai o ngā me ngā āhuatanga. Hēura hoahoa plurality o ngā huānga image kopakia ana i roto i te tapawhā tohu te huinga ao (U). Engari o porowhita e taea hoki te whakamahi i ētahi atu tau kati, engari tonu te mauri te taua. whakawhiti Whika ki ia atu, rite ki tikanga o te raruraru (i roto i te take tino whānui). Hoki, kia tapanga nga whika raraunga i runga i. Ka rite ki kia mahi i te mea timatanga i raro i whakaaro huinga ngā tū i roto i te wāhanga rerekē o te hoahoa. I runga i taea reira whakamarumaru he wāhi motuhake, reira te faataaraa ia te huinga hou i hanga.

Ki te huinga raraunga ko reira whakaaetia ki te mahi i taketake ngā mahi pāngarau: tua (moni o nga huinga o ngā huānga), tangohanga (rerekētanga), whakareatanga (hua). I tua atu, whakawhetai ki te hoahoa Hēura-Venn taea te mahi ngā mahi i runga i te whakarite i whakaritea ki te maha o ratou huānga Pākēha, kore ake e whakairia ki a ratou.