Kodi kumvetsa chifukwa chake "kuphatikiza" kuti "zoipa" amapereka "opanda"?

Kumvetsera mphunzitsi wa masamu, ambiri mwa ophunzirawo kuzindikira zinthu monga axiom ndi. Koma anthu ochepa kuyesera kuti afike pansi ndi kupeza chifukwa "opanda" kuti "kuphatikiza" amapereka "opanda" chizindikiro, ndipo pamene kuchulukitsa chiwerengero awiri zoipa akutuluka positive.

malamulo a masamu

achikulire ambiri sindingakhoze kufotokoza kuti iwo kapena ana awo chifukwa chake zili choncho. Iwo molimba kumvetsa nkhani sukulu, koma zilibe ngakhale kuyesa kupeza kumene anachita malamulo amenewa. Ndipo zifukwa zomveka. Nthawi zambiri, ana a masiku ano si choncho m'chimbulimbuli, iwo ayenera pansi ndi kumvetsetsa, mwachitsanzo, chifukwa "kuphatikiza" kuti "zoipa" amapereka "opanda". Ndipo nthawizina urchins mwachindunji mafunso lachinyengo, kuti asangalale nthawi imene akulu sangapereke yankho lomveka bwino. Ndipo zosafunikira ngati mphunzitsi wachinyamata ikatitimira ...

Zodabwitsa ndizakuti, tisaiwale kuti tatchulawa ulamuliro ndi zothandiza chulutsa ndi fission. The mankhwala a manambala zoipa ndi zabwino zokha "kupereka opanda. Ngati pali manambala awiri ndi chizindikiro "-", chifukwa ndi chiwerengero positive. N'chimodzimodzinso magawano. Ngati mmodzi wa manambala adzakhala oipa, ndiye quotient kudzakhala ndi chizindikiro "-".

Kufotokoza kulondola lamulo la masamu, m'pofunika zopanga za axiom mphete. Koma ayenera kuzindikira chimene icho chiri. Mu masamu otchedwa mphete imene ntchito awiri kukhuzidwa ndi zinthu ziwiri. Koma kumvetsa bwino chitsanzo.

axiom mphete

Pali malamulo angapo masamu.

• The woyamba commutative, malinga ndi iye, C + V = V + C.
• wachiwiri amatchedwa associative (V + C) + D = V + (C + D).

Iwo amamvera ndi chulutsa (V × C) × D = V × (C × D).

Palibe zimafika ndi malamulo oti poyera bulaketi (V + C) × D = V × D + C × D, ndi zoona kuti C × (V + D) = C × V + C × D.

Komanso, anapezeka kuti mphete angalowe wapadera ndale ndi Kuwonjezera wa chinthu chimene ndi ntchito yomwe izi ndi zoona: C + 0 = C. Komanso, aliyense zosiyana C ndi mfundo akhoza ikhale (-C). Choncho C + (-C) = 0.

Deducing axioms kwa manambala olakwika

? Mutayamba mawu pamwambapa, n'zotheka muyankhe funso ili: "" kuphatikiza "kuti" zoipa "apereka chizindikiro chilichonse" Kudziwa axiom za chulutsa manambala zoipa, muyenera kutsimikizira kuti ndithu (-C) × V = - (C × V). Komanso, choonadi ndi wofanana: (- (- C)) = C.

Kuti tichite zimenezi, choyamba tiyenera kutsimikizira kuti aliyense wa zanyengo pali zosiyana iye yekha "mbale." Taonani umboni izi. Tiyeni tiyese kuganizira zimene a C popenyana ndi manambala awiri - V ndi D. Kuchokera ndizoonekeratu kuti C + V = 0 ndipo C + D = 0 mwachitsanzo, C + V = 0 = C + D. Pokumbukira malamulo commutative ndi pa katundu wa manambala 0, tingaganizire Uwerenge manambala onse atatu: C, V, ndipo yesani kupeza phindu D. V. N'zosatheka V = V + 0 = V + (C + D) = V + C + D, kuyambira mtengo wa C + D, Analeredwa monga pamwambapa, liri 0. Choncho, V = V + C + D.

Mofananamo, phindu linanena bungwe ndi D: D = V + C + D = (V + C) + D = 0 + D = D. Izi zimaonekeratu kuti V = D.

Pofuna kumvetsa chifukwa onse "kuphatikiza" kuti "zoipa" amapereka "opanda", m'pofunika kumvetsa mfundo zotsatirazi. Choncho, mchitidwe (-C) ali otsutsana ndi C (- (- C)), i.e. iwo ndi ofanana ndi mnzake.

Ndiye n'zachionekere kuti 0 × V = (C + (-C)) = C × V × V + (-C) × V. Kuchokera ndizoonekeratu kuti C × V oppositely (-) C × V Choncho, (- C) × V = - (C × V).

Kuti wathunthu rigor masamu ayenera amatsimikizanso kuti 0 × V = 0 kuti mbali iliyonse. Ngati mutsatira nzeru, ndiye 0 × V = (0 + 0) X 0 × V = V + 0 × V. Izi zikutanthauza kuti Kuwonjezera wa mankhwala 0 × V sasintha kuchuluka zinalembedwa. Pambuyo ntchito zonsezi ndi ziro.

Podziwa zonse axioms amenewa anachokera osati monga "kuphatikiza" kuti "zoipa" amapereka, koma amene analandira ndi kuchulukitsa chiwerengero negative.

Chulutsa ndi gulu la manambala awiri ndi chizindikiro "-"

Popanda kupita mokoma masamu, mungayesere njira chosavuta kufotokoza malamulo a kanthu ndi manambala negative.

Musamachite C - (-V) = D, tsiku lino, C = D + (-V), i.e. C = D - V. Ife kusamutsa ndi V tikuona kuti C + V = D. Ndiko kuti, C + V = C - (-V). Mwachitsanzo Ichi n'chifukwa mawu, kumene kuli awiri "opanda" mu mzere, anati zizindikiro ayenera kusinthidwa kuti "kuphatikiza". Tsopano tiyeni kuthana ndi kuchulukitsa.

(-C) × (-V) = D, mu akuti mukhoza kuwonjezera ndi kuchotsera zidutswa ziwiri zofanana kuti sadzasintha kufunika kwake: (-C) × (-V) + (C × V) - (C × V) = D.

Tiyeni tikumbukire malamulo a ntchito chakudya, ife kupeza:

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

2) (-C) × ((-V) + V) + C × V = D;

3) (-C) + C × 0 × V = D;

4) C × V = D.

Kuchokera pamenepa, ndizoonekeratu kuti C × V = (-C) × (-V).

Mofananamo, munthu angakhoze kutsimikizira kuti chifukwa cha kugawikana kwa manambala awiri zoipa ndithu.

General malamulo masamu

Kumene, zimenezi si kwaana m'sukulu za pulayimale amene akungoyamba kumene kuphunzira umboni manambala negative. Iwo kulibwino kufotokoza cholinga looneka zikugwira akuti kuwadziŵa kudzera pagalasi. Mwachitsanzo, anatulukira, koma palibe zidole alipo alipo. Iwo akhoza anasonyeza ndi chizindikiro "-". Chulutsa zinthu ziwiri transmirror nawatengera iwo ku dziko lina, limene ndi wofanana lero, ndiye zotsatira zake, tili ndi manambala positive. Koma chulutsa umboni chiwerengero zoipa ndi zabwino amapereka zotsatira kokhaku onse. Ndipotu, "kuphatikiza" kuchulukitsa ndi "opanda" amapereka "opanda". Komabe, mu sukulu za pulayimale zaka ana si kuyesera kulowa mokoma onse masamu.

Ngakhale, ngati inu choonadi, kwa anthu ambiri, ngakhale ndi maphunziro apamwamba anakhalabe chinsinsi malamulo ambiri. Zonse zimatengera mokhazikika kuti aphunzitsi kuwaphunzitsa, osati kwambiri vuto wofufuza mavuto onse chibadidwe masamu a. "Wachisoni" kuti "zoipa" amapereka "kuphatikiza" - aliyense akudziwa za izo, popanda yekha. Zili choncho chifukwa lonse, ndi manambala fractional.