Kanjani ukuqonda ukuthi kungani "plus" ukuze "omubi" unikeza "lokususa"?

Ukulalela uthisha wezibalo, iningi labafundi ukuqonda izinto njengenhlangano Axiom. Kodwa bambalwa abantu bezama emnyombweni futhi uthole ukuthi kungani "lokususa" ukuze "plus" kunikeza uphawu "lokususa", futhi lapho siphindaphindeka izinombolo ezimbili ezimbi uyaphuma omuhle.

imithetho wezibalo

Iningi labantu abadala abakwazi ukuchaza bona noma izingane zabo ukuthi kungani kunjalo. Babekholelwa ngokuqinile ukuqonda impahla esikoleni, kodwa lokho akusho ngisho ukuzama ukuthola ukuthi lapho wenza leyo mithetho. Futhi ukuzonda ngesizathu esihle. Ngokuvamile, izingane zanamuhla ziyizikhali kalula kanjalo, badinga emnyombweni futhi ukuqonda, isibonelo, kungani "plus" ukuze "omubi" unika "lokususa". Futhi ngezinye izikhathi urchin ukubuza ngqo imibuzo olukhohlisayo, ukuze, ujabulela isikhathi lapho abantu abadala abakwazi ukunikeza impendulo ecacile. Futhi kunendaba ngempela uma uthisha osemusha Ufika abanjwe ...

Phela, kufanele kuphawulwe ukuthi umthetho oshiwo ngenhla siyasebenza ngoba ukubuyabuyelela kanye ukuqoqwa. Umkhiqizo we izinombolo engemihle futhi omuhle kuphela "ukunikeza lokususa. Uma kukhona izinombolo ezimbili uphawu "-", umphumela uba inombolo efanele. Kuyefana nasendleleni ukuhlukana. Uma enye yezinombolo izokhombisa ukuthi akanalo igciwane, ngakho-ke quotient beyoba uphawu "-".

Ukuchaza ngokunemba umthetho wezibalo, kubalulekile nokuba akuhlele emasongweni Axiom. Kodwa kufanele siqale siqonde ukuthi kuyini. Esifundweni sezibalo okuthiwa indandatho isethi lapho imisebenzi emibili bahilelekile izici ezimbili ngokuyinhloko. Kodwa ukuqonda kangcono nge isibonelo.

Axiom indandatho

Kukhona imithetho eziningana zezibalo.

• Eyokuqala yalezi commutative, ngokusho kwakhe, C + V = V + C.
• Eyesibili libizwa associative (V + C) + D = V + (C + D).

Futhi uyalalela futhi ukubuyabuyelela (V x C) x D = V x (C x D).

Akekho kukhanselwe futhi imitsetfo leyengamele ubakaki evulekile (V + C) x D = V x D + C x D, kuyiqiniso ukuthi C x (V + D) = C x V + C x D.

Ngaphezu kwalokho, kwatholakala ukuthi iringi Ungafaka hlangothi ekhethekile ukwengeza i-elementi, ukusetshenziswa lapho okulandelayo kuyiqiniso: C + 0 = C. Ngaphezu kwalokho, ngayinye C okuphambene liyisici ukuthi kungenziwa azibiza ngokuthi (-C). Ngakho C + (-C) = 0.

Deducing axioms izinombolo negative

? Ngokwamukela izitatimende ezingenhla, kungenzeka ukuba uphendule umbuzo othi: " 'plus" ukuze "omubi" enikela nganoma iyiphi uphawu "Ukwazi Axiom mayelana ukubuyabuyelela izinombolo negative, udinga ukuqinisekisa ukuthi V ngempela (-C) x = - (C x V). Futhi, lokho kuyiqiniso ilingana: (- (- C)) = C.

Ukuze wenze lokhu, kuqala esinalo ukufakazela ukuthi ngamunye izakhi kukhona omunye malungana naye kuphela "umzalwane." Cabangela ubufakazi obulandelayo. Ake sizame ukubona ngeso lengqondo ukuthi okuphambene C izinombolo ezimbili - V no D. Kule kusobala ukuthi C + V = 0 no-C + D = 0, okusho C + V = 0 = C + D. Ekhumbula umthetho commutative futhi phezu izakhiwo izinombolo 0, singacabangela isamba sazo zonke izinombolo ezintathu: C, V, bese uzama ukuthola ukuthi ukubaluleka D. V. Uma ucabangisisa, V = V + 0 = V + (C + D) = V + C + D, kusukela ukubaluleka C + D, akhethwa njengosuku ngenhla, kuba ukuqinisela 0. Ngakho, V = V + C + D.

Ngokufanayo, inani okukhipha futhi D: D = V + C + D = (V + C) + D = 0 + D = D. Kule, kuba sobala ukuthi V = D.

Ukuze uqonde ukuthi kungani zonke "plus" ukuze "omubi" inika "lokususa", kubalulekile ukuqonda okulandelayo. Ngakho, i-elementi (-C) abaphikisa futhi C (- (- C)), isb ayalingana nomunye.

Khona-ke kusobala ukuthi 0 x V = (C + (-C)) = C x V x V + (-C) x V Kule kusobala ukuthi C x V oppositely (-) C x V, ngakho-ke, (- C) x V = - (C x V).

Ukuze uthole ngokuphelele okukhulu zezibalo kumele uqinisekise ukuthi 0 x V = 0 nganoma yisiphi isici. Uma ulandela logic ke 0 x V = (0 + 0) x 0 x V = V + 0 x V Lokhu kusho ukuthi ngaphezu komkhiqizo 0 x V ayishintshi emalini ebekiwe. Ngemva kwawo wonke lo msebenzi zero.

Ukwazi konke lokhu axioms kungenziwa etholakala hhayi kuphela ngokuthi "plus" ukuze "omubi" unika, kodwa ukuthi etholwe siphindaphindeka izinombolo engemihle.

Ukubuyabuyelela nokuhlukanisa wezinombolo ezimbili uphawu "-"

Ngaphandle kokuya ezicashile zezibalo, ungazama ngendlela elula ukuchaza imithetho senzo izinombolo engemihle.

Ucabange ukuthi C - (-V) = D, ngesisekelo salokhu, C = D + (-V), isb C = D - V Thina uthumele futhi V sibona ukuthi C + V = D. Okungukuthi, C + V = C - (-V). Lesi sibonelo uchaza ukuthi kungani le nkulumo, lapho kukhona "lokususa" ezimbili zilandelana, kusho izimpawu kufanele zishintshwe ukuze 'plus ". Manje ake ukubhekana ukubuyabuyelela.

(-C) x (-V) = D, kule nkulumo ingasho ungeze futhi ukhiphe izingcezu ezimbili ezifanayo ukuthi ngeke kushintshe ukubaluleka kwalo: (-C) x (-V) + (C x V) - (C x V) = D.

Asikhumbule imithetho yokusebenza okuyisisekelo, sithola:

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.

Kule kusobala ukuthi C x V = (-C) x (-V).

Ngokufanayo, umuntu angabona ukuthi likhona ngenxa division of izinombolo ezimbili ezimbi ngeke kahle.

Imithetho General zezibalo

Yiqiniso, le ncazelo asifanele esikoleni samabanga aphansi abantwana abakhula ngaphansi kwayo ukuthi usanda kuqala ukufunda izinombolo abstract ezimbi. Zazisho kangcono achazele into ebonakalayo, nokukhohlisa eside ajwayelekile kubo ngokusebenzisa esibukweni. Ngokwesibonelo, yasungulwa, kodwa akukho amathoyizi ezikhona lapho. Nabo futhi ingaboniswa uphawu "-". Ukubuyabuyelela bezinto ezimbili transmirror uyisa uzifake kwenye emhlabeni, okuyinani elilingana kuze kube manje, okungukuthi, ngenxa yalokho, siba izinombolo omuhle. Kodwa ukuphindwaphindwa inombolo abstract omubi ku-positive unika imiphumela kuphela laziwe kubo bonke. Phela, "plus" iphindwe "lokususa" unikeza "lokususa". Nokho, e- primary school yobudala izingane kungukuthi kakhulu bezama ukuthola kuwo wonke umehluko wemisindo nemiqondo yamagama zezibalo.

Nakuba, uma sibhekane neqiniso, abantu abaningi, ngisho imfundo ephakeme ayikaziwa imithetho eminingi. Zonke kuthatha kalula ukuthi othisha babafundise, hhayi nzima kakhulu lokumba kobunzima esivela wezibalo. "Negative" ukuze "omubi" unika "plus" - wonke umuntu uyazi ngakho, ngaphandle kokukhetha. Lo is njengoba yiqiniso wonke, futhi izinombolo wamaqhuzu.