Kuyini inombolo ephelele engaphezulu kweqanda? Umlando, ububanzi, izici

Izibalo uhlukane nefilosofi jikelele cishe ekhulwini lesithupha leminyaka BC. e., futhi kusukela ngaleso sikhathi-ke liqala ukuzungeza kwayo okunqobayo emhlabeni wonke. Esigabeni ngasinye ukuthuthukiswa alethwe into entsha - i-akhawunti zokucathula kwazivelela, siguqulelwa umehluko kanye calculus ebalulekile, ekhulwini alternated, ifomula babeba yibe yinto exakayo, futhi kufike isikhathi lapho "ekuqaleni izibalo nzima kakhulu -. Wanyamalala kuzo zonke izinombolo" Kodwa yilokho okwakuseza ngemuva?

I yokuqalisa

Izinombolo bemvelo babengebona abafowabo belingana imisebenzi yokuqala zezibalo. Uma emuva, amabili emuva, ezintathu emgogodleni ... Bavele sibonga usosayensi Indian ngubani baletha positional inombolo system. Igama elithi "positional" kusho ukuthi indawo idijithi ngayinye eziningana ngokuqinile kuchazwa futhi oluhambisana esigabeni sayo. Ngokwesibonelo, izinombolo 784 kanye 487 - izinombolo ziyafana, kodwa izinombolo azifani njengoba wangaphambili kuhlanganisa 7 zamakhulu, kanti owesibili - 4. kuphela amaNdiya Ukuqamba wacosha Arabhu owakhuphula inani izinhlobo siyazi Manje.

Ezikhathini zasendulo, izinombolo enamathiselwe ukubaluleka ezingaqondakali, sezibalo esikhulu kunazo zonke Pythagoras babekholelwa ukuthi inombolo kuwumgogodla sokudalwa belingana izakhi eziyisisekelo - umlilo, amanzi, umhlaba, umoya. Uma sicabanga ngakho konke kuphela ngohlangothi zezibalo ke ukuthi inombolo ephelele engaphezulu kweqanda? Inkambu izinombolo zemvelo luchazwa ngokuthi N futhi kuyinto uchungechunge esingapheliyo izinombolo ukuthi kukhona integers omuhle futhi 1, 2, 3, ... + ∞. Zero isikhishiwe. Ikakhulu esetshenziselwa ngokubala izinto futhi ucacise i-oda.

Uyini inombolo yemvelo izibalo? axioms ka Peano

Field N base lapho oba wezibalo aphansi. Ngokuhamba kwesikhathi, ezicezile ensimini integers, izinombolo okunengqondo, eqela.

Umsebenzi sezibalo Italian Dzhuzeppe Peano kwenza kwaba nokwenzeka ukwakhiwa obengeziwe izibalo, kwamenza okusemthethweni futhi zalungiselela iziphetho eminye ukuthi uhambe ngalé N. esifundeni ensimini Yini inombolo wemvelo, kuye kwatholakala ngaphambilini ngolimi olulula, okulandelayo kuzoxoxwa ngesisekelo incazelo zezibalo we Peano axioms.

• Unit zithathwa njengeziNdawo ezingamaGugu inombolo zemvelo.
• Inombolo elandela inombolo yemvelo, kuyinto engokwemvelo.
• Ngaphambi iyunithi Ayikho inombolo zemvelo.
• Uma b inombolo kumele kube kokubili c inombolo, futhi inani d ke c = d.
• I Axiom ka lokungeniswa, nakho kusikisela ukuthi inombolo yemvelo, uma isitatimende ukuthi izinsiza ezincike ipharamitha kuyiqiniso for inombolo 1, bese sicabanga ukuthi lusebenza inombolo n amasimu izinombolo zemvelo N. Khona egomela kuyiqiniso ngoba n = 1 kusukela emkhakheni izinombolo zemvelo N.

imisebenzi Basic enkambini izinombolo yemvelo

Kusukela N ensimini waba ngowokuqala izibalo, kuba kwakufanele uphathwe njengongcwele esizindeni definition, futhi endaweni ngezansi inani ukuthengiselana amagugu. Basuke ivaliwe futhi akukho. Umehluko omkhulu wukuthi ukusebenza Siyaqiniseka ukushiya yi avaliwe ngaphakathi isethi N, kungakhathaliseki ukuthi behileleka izinombolo. Kwanele ukuthi zingabantu zemvelo. Umphumela asele ukuxhumana zezinombolo akuyona kuqonde futhi kube kuncike yokuthi labo abathintekayo ethi, njengoba kungase kube ngokuphambene definition eziyisisekelo. Ngakho, imisebenzi ivaliwe:

• Ukwengezwa - x + y = z, lapho x, y, z ivela ensimini N;
• ukubuyabuyelela - x * y = z, lapho x, y, z ivela ensimini N;
• Exponentiation - x ^y, lapho x, y ivela N. Field

Imisebenzi ezisele, umphumela ezingasetshenziswa akekho ekutholweni umongo "okungukuthi inombolo wemvelo" ngendlela elandelayo:

• Khupha - x - y = z. Field izinombolo zemvelo kuyivumela kuphela uma eside x y;
• division - x / y = z. Field izinombolo zemvelo kuyivumela kuphela uma z lihlukaniswe by y akukho zinsalela, isb ngokulinganayo.

Izakhiwo izinombolo, okuqondene N ensimini

Zonke ukucabanga okwengeziwe zezibalo kuyoba ngokohlelo lweSitatimende lezi izakhiwo, eziwubala kakhulu, kodwa akukho ebaluleke kancane.

• umukghwa wokuhlanekezela - x + y = y + x, lapho inani x, y kufakwe ibhokisi N. Noma owaziwa "kusukela Ukuthuthela isamba aliguquki."
• umukghwa zokuphindaphinda - x * y = y * x, lapho izinombolo x, y ivela N. Field
• impahla associative kokuhlanganisa - (x + y) + z = x + (y + z), lapho x, y, z ivela N. Field
• impahla associative zokuphindaphinda - (x * y) * z = x * (y * z), lapho izinombolo x, y, z ivela N. Field
• impahla wokusakaza - x (y + z) = x * y + x * z, lapho izinombolo x, y, z ivela N. Field

Uhlu Pythagoras

Esinye sezinyathelo zokuqala nolwazi abafundi kulo lonke aphansi wezibalo izakhiwo ngemva kokuba baqonde wona ngokwawo ukuthi izinombolo abizwa ngokuthi yemvelo, kuyinto ithebula Pythagoras. Kungaba kubhekwe hhayi kuphela kusukela umbono wesayensi, kodwa futhi njengendlela lesikhumbuzo ezibalulekile zesayensi.

Leli thebula ukubuyabuyelela usebhekene izinguquko eziningi ngokuhamba kwesikhathi: kususiwe zero, futhi izinombolo kusuka 1 kuya 10 amele ngokwabo, ngaphandle oda ezidlula (zamakhulu, izinkulungwane ...). Kuyinto itafula lapho izihloko lemigqa namakholomu - inombolo bese okuqukethwe emangqamuzaneni empambana ilingana umkhiqizo eyabo.

Esikhathini umkhuba wokuqeqesha mashumi eminyaka ambalwa okugcina kwakukhona isidingo ukufunda etafuleni Pythagorean "ukuze", okungukuthi, kuqala waqhubeka ngekhanda. Ukubuyabuyelela 1 yakhishwa, kusukela yi ilingana 1 noma ngaphezulu isici. Phakathi naleso sikhathi, etafuleni kungabonwa ne nqunu iso iphethini: umkhiqizo inani elandayo ngesinyathelo esisodwa, okuyinani elilingana isihloko yezinhlamvu. Ngakho, isici sesibili usibonisa kukangaki udinga ukuthatha kuqala, ukuze bathole umkhiqizo oyifunayo. Lolu hlelo akafani omunye kuwusizo kakhudlwana eyayisetshenziswa Ephakathi: uyamazi ukuthi inamba omuhle, futhi indlela ewubala nje, abantu bakwazile izinkinga ngokwakho kwansuku ngokusebenzisa uhlelo yayisekelwe lamadigri ezimbili.

A isethi engezansi njengesizinda sombuso wezibalo

Okwamanje, emkhakheni izinombolo zemvelo N kubhekwa kuphela njengoba omunye subsets yezinombolo eziyinkimbinkimbi, kodwa akuwenzi asilutho kwezesayensi. inombolo Yemvelo - into yokuqala ukuthi ingane ifunda ngokutadisha thina futhi kuwo wonke umhlaba osizungezile. Uma umunwe, ezimbili umunwe ... Siyabonga kuye, indoda ezakhiwe ukucabanga okunengqondo, kanye nekhono ukuze kutholakale imbangela nomphumela kwezintathu zomkhiqizo, kuvuleke indlela yokuba okutholakele ezinkulu.