Izigaba zamanani: imbali, inkcazelo, izakhiwo ezisisiseko

Iimpawu ezilula zemathematika zaziwa kubantu nakumaxesha amandulo. Ngelo xesha, kwakukho ukuphucula okuqhubekayo kokubili imisebenzi kunye nokurekhoda kwabo kwenye okanye enye.

Ngokukodwa, kwiYiputa yamandulo, izazinzulu zazo zenze igalelo elikhulu ekuphuhliseni i-arithmetic yamandulo, kunye nokudala iziseko ze-algebra kunye nejometri, zibonisa ukuba xa inani liphindwe inani elifanayo kaninzi, Kuthatha umthamo omkhulu wenzame engadingekile. Ukongezelela, olo hlobo lukhokelela kwiindleko ezinkulu zemali: ngokubhekiselele kwizicwangciso ezisebenzayo zokuyila naziphi na iirekhodi, ngasinye isenzo kunye nenani kufuneka sichazwe ngokuchanekileyo. Ukuba sikhumbula ukuba i-papyrus elula kakhulu ibangela imali enomdla kakhulu, ngoko akufanele imangalise imizamo eyenziwe yiYiputa ukuba ifune indlela yokuphuma kule meko.

Isisombululo safunyanwa nguDiophantus owaziwayo wase-Aleksandriya, owaza kunye nomqondiso obalaseleyo weemathematika owaqala ukubonisa ukuba zihlandlo eziliphi na eziyimfuneko ukwandisa le okanye loo nombolo ngokwayo. Emva koko, isazi sezibalo seFrench R. Descartes esaziwayo safezekisa ukubhala kweli binzana, icetyisa ukuba xa kuchaza amandla amanani, yabekezela ekhoneni eliphezulu lasekunene kunombolo enkulu.

Isigqibo sokugqibela ekubhaliseni kwinqanaba leenombolo yinto yomsebenzi owaziwayo uN. Schücke, owathumela umgangatho wokuqala kunye ne-degrees zero kwi-revolution yesayense.

Kuthetha ukuthini igama elithi "ukwakha idideli"? Okokuqala, kuyimfuneko ukuqonda ukuba ukucacisa ngokwayo ngenye yezona zinto zibaluleke kakhulu ekusebenzeni kwemathematika, okubalulekileyo ekuququzeleleni ngokuphindaphindiweyo inamba ngokwayo.

Ngokuqhelekileyo, lo msebenzi uchazwa yintetho ethi "XY". Kule meko, "X" iya kuthiwa isiseko se-degree, kwaye "Y" iya kubizwa ngokuba yiyo. Kule meko, "ukuphakanyiswa kumandla" kunokucatshulwa ngokuthi "phinda" X "ngokwayo" Y "amaxesha."

Iidridi zamanani, njengamanye amanqaku eemathematika, zinezakhiwo ezithile:

1. Xa ufika kwigunya le-zero kwanoma iyiphi inamba eyahlukileyo ukusuka kwi-zero (zombini ilungile kwaye ayibi), enye iya kufumaneka.

X ^^ 0 = 1

2. Iidridi zamanani, apho izikhombisi zinenani elingafanelekanga, kufuneka ziguqulwe zibe ngongoma kunye nesalathisi esihle

X-a = 1 / x ^ a

3. Ukuze kuqinisekiswe ukuphindaphinda kwamanani kunye namagunya, kufuneka kukhunjulwe ukuba lo msebenzi unokwenzeka kuphela xa unesiseko esisodwa. Kule meko, ukuphindaphinda kwamanani kunye namagunya kwenziwa ngokuhambelana nalo mgaqo olandelayo: isiseko asihlali sitshintshile, kwaye kumntu omnye, ukubaluleka kweempawu zamandla aseleyo zongezwa.

X ^ yx ^ z = x ^ y + z

4. Kwimeko apho amadidi ahlukeneyo, kuyimfuneko ukulandela umgaqo ofanayo, kodwa endaweni yesibalo kwizinto ezibonakalayo kuya kubakho umahluko.

X ^ y / x ^ z = x ^ yz

5. Elinye ipropati ebalulekileyo yee-degrees idibene nezo meko xa kufuneka ukuba kuphakanyiswe amandla okuzimela ngokwawo. Kule meko, kubalulekile ukwandisa zombini ezi zikhombisi.

(X ^ y) ^ z = x ^ yz

6. Kwezinye iimeko kukho imfuneko yokubhala phantsi iqondo lemveliso ngokwemigangatho yamanani. Kule mfuneko kuyimfuneko ukukhumbula ukuba umlinganiselo wemveliso ubalwa ngokuhambelana nalo mgaqo:

(Xyz) ^ a = x ^ ay ^ az ^ a

7. Ukuba kukho isidingo sokubhalela umgangatho we-quotient, into yokuqala ekufuneka uyiqaphele kukuba isiseko se-denominator ayikwazi ukuba yinto. Kwiminye imfuneko kubambelele kule fomyula elandelayo:

(X / y) ^ a = x ^ a / y ^ a

Iingxaki ezithile zidibeneyo xa kufuneka ukuba ziphakanyiswe kumbane isiseko esichazwe ngaphantsi kwesantya. Isiphumo kule meko sinokuthi sibi okanye sihle. Kuya kuxhomekeka kumboniso, oko kukuthi, kwiyiphi inamba-engavamile okanye mhlawumbi-le nqondiso.