Me pēhea te ki te matau he aha te "me" ki "tōraro" homai te "tango"?

Whakarongo ki te kaiako o pāngarau, te nuinga o nga ākonga kite te rauemi hei axiom. Otiia torutoru iwi e ngana ana ki te tiki i ki te raro, me te kitea i roto i te "tango" ki "me" homai aha te "tango" tohu, a ka whakanuia e rua ngā tau kino mai i roto i pai.

nga ture o te pāngarau

e kore e taea e te nuinga o ngā pakeke whakamārama ki a ratou ano ki o ratou tamariki ranei, he aha te mea na tenei. Ratou mau taa te rauemi i roto i te kura, engari e kore e noa tamata i te reira ki te kitea i roto i te wahi i enei ture. A mo te take pai. E mea pinepine, e kore e pera heahea tamariki a tenei ra, Me ratou ki te tiki ki te raro, me te ki matau, mo te tauira, he aha te "me" ki "tōraro" homai "tango". Na te tahi mau taime te ui āta kina pātai uaua, i roto i te tikanga ki te oaoa i te wa, ka kore e taea te hoatu ngā pakeke i te mārama whakahoki. A tino mea faufaa te reira, ki te mau te kuao kaiako tangata e ...

Ratau, kia tuhia te reira e te mea whai hua hoki te whakareatanga, me te mo wehenga te tikanga i runga ake-whakahuatia. Ko te hua o te tau tōraro, me te pai anake "hoatu he, haunga te. Ki te mea i reira e rua tau ki te tohu "-", te hua ko te tau tōrunga. Ko te taua pā ki te wehenga. Ki te kotahi o nga tau ka kia kino, katahi ka waiho hoki te huawehe ki te tohu "-".

Hei whakamārama i te tika o te ture o pāngarau, he mea e tika ana ki te hanga i te mowhiti axiom. Engari kia matau te tuatahi te mea ko reira. I roto i te pāngarau i huaina huinga mowhiti i roto i i whai wāhi e rua ngā mahi ki ngā āhuatanga e rua. Otiia ki te matau i te reira pai ki te tauira.

mowhiti axiom

He maha ngā ture pāngarau.

• Ko te tuatahi o enei āpiti, kia rite ki a ia, = C + V V + C.
• huaina te tuarua ko herekore (V + C) + D = V + (C + D).

Ratou pupuri hoki, me te whakareatanga (V x C) x D = V x (C x D).

Tangata whakakorea me ngā ture e ai te taiapa tuwhera (V + C) x D = V C x D x D +, he pono ano hoki reira e C x (V + D) = C x V + C x D.

I tua atu, i kitea ai e taea te mowhiti tomo te kūpapa motuhake i tua o te huānga, he pono te whakamahi o nei te whai ake: C + 0 = C. I tua atu, hoki ko ia te ritenga atu C he huānga e taea te whakaritea rite (-C). Ko te kupu C + (-C) = 0.

Te kimi i axioms mō ngā tau tōraro

? E ohi i te tauākī i runga, he taea reira ki te whakahoki i te pātai: "" me "ki" tōraro "homai tetahi tohu" E matau te axiom e pā ana ki te whakarea o ngā tau tōraro, e hiahia ana koe ki te whakaū e pono (-C) x V = - (C x V). A hoki, he aha te mea pono he rite: (- (- C)) = C.

Ki te mahi i tenei, i te tuatahi i tatou ki te whakamatau e ia o nga mea timatanga i reira he kotahi ritenga ia anake "teina." A feruri i te taunakitanga e whai ake nei. Kia tamata o ki te whakaaro he aha te ritenga atu C e rua tau - V me D. Mai i tenei whai reira e C + V = 0 me C + D = 0, arā C + V = 0 = C + D. te haamana'oi te te ture āpiti, me te i runga i nga āhuatanga o nga tau 0, ka taea e tatou whakaaro te moni o tau e toru katoa: C, V, ka ngana ki te kitea i roto i te uara o D. V. hono totonú, V = V + 0 = V + (C + D) = V + C + D, mai te uara o te C + D, i tangohia rite te runga ake, ōrite reira 0. No reira, V = V + C + D.

Waihoki, ko te uara putanga me mo D: D = V + C + D = (V + C) + D = 0 + D = D. Mai tenei, riro te reira mārama e V = D.

I roto i te tikanga ki te mahino aha katoa te "me" ki "tōraro" homai he "haunga", he mea e tika ana ki te matau i te whai. Ko te kupu, hoki te huānga (-C) e hoariri me C (- (- C)), i.e. e rite ki tahi i te tahi ratou.

Na ka ko reira kitea e 0 x V = (C + (-C)) = C x + V x V (-C) x V. i tenei whai reira e C x V oppositely (-) C x V, reira, (- C) x V = - (C x V).

Hoki te nanakia pāngarau oti me hoki whakaū e 0 x V = 0 mō tetahi huānga. Ki te whai koe i te arorau, ka 0 x V = (0 + 0) x 0 x V = V + 0 x V. tikanga tenei e kore e te tua o te hua 0 x V huri te nui whakaritea. I muri i tenei mahi katoa ko te kore.

E matau katoa o enei axioms taea te ahu e kore anake rite te "me" ki "tōraro" homai, engari e whiwhi e whakanuia tau tōraro.

Whakarea me te wehenga o rua tau ki te tohu "-"

Te kore te haere ki roto ki te mita pāngarau, ka taea e koe te tamata i te ara ohie ki te whakamārama i te ture o te mahi ki te tau tōraro.

Me kī, i taua C - (-V) = D, i runga i tenei pütake, C = D + (-V), i.e. C = D - V. whakawhiti matou me V kite tatou e C + V = D. Ko, te C + V = C - (-V). E whakamārama ana tēnei tauira he aha te faaiteraa, te wahi i reira e rua "tango" i roto i te rarangi, ka mea kia puta ke nga tohu mō "me". Na kia mahi a ki te whakarea.

(-C) x (-V) = D, i roto i te faaiteraa e taea te tāpiri i me te tango rua nga wahi ōrite kore e e huri i tona uara: (-C) x (-V) + (C x V) - (C x V) = D.

Kia mahara tatou ki nga ture o te mahi tino, whiwhi tatou:

1) (-C) x (-V) + (C x V) + (-C) x V = D;

2) (-C) x ((-V) + V) + C x V = D;

3) (-C) + C x 0 x V = D;

4) C x V = D.

Mai i tenei whai reira e C x V = (-C) x (-V).

Waihoki, ka taea e tetahi te whakamatau e te hua o te wehenga o ngā tau tōraro e rua e pai.

General ture pāngarau

O te akoranga, e kore te mea e tika ana mō ngā tamariki kura tuatahi e tika tīmata ki te ako i ngā tau kino waitara tenei whakamārama. pai ratou hiahia whakamārama ki te ahanoa kitea, raweke wā maori ki a ratou i roto i te whakaata. Hei tauira, whakaaro, engari he reira kahore tākaro ngā. taea te whakaatu i ratou me ki te tohu "-". Whakarea o ngā rua transmirror mauranga ratou ki tetahi ao, i te mea e rite ana ki te hakari, e ko, rite ki te hua, to tatou tau pai. Ko te whakarea o te tau tōraro waitara ki te pai homai hua anake mohiotia ki katoa. I muri i te katoa, te "me" whakanuia e "haunga" homai te "tango". Heoi, i roto i te kura tuatahi ake e kore e tamata rawa tamariki ki te tiki ki te mita pāngarau katoa.

Ahakoa, ki te kanohi koe te pono, mo te iwi maha, ara ki te mātauranga teitei noho te mea ngaro maha ture. Katoa e te reira no te homai e whakaako kaiako ratou, e kore rawa nui te raruraru ki te ruku hōhonu ki te mau fifi katoa tūturu i roto i te pāngarau. "Negative" ki "tōraro" homai "me" - mohio katoa e pā ana ki reira, kahore he okotahi. Ko rite pono mo te katoa, a mo tau hautanga tenei.