Amanani Real neempawu zazo

KaPythagoras bathi inani kwaba sekusekweni kwehlabathi kwi belingana izinto ezinkulu. UPlato wayekholelwa ukuba inani amakhonkco isenzeko kunye noumenon, ukunceda ukuba ukwazi, ukuze kulinganiswe yaye ukufikelela kwizigqibo. Izibalo livela elithi "arifmos" - inani, loqalo lwencopho kwimathematika. Kuyenzeka ukuchaza nayiphi na into - sabaqalayo kwiindawo abstract apile.

Needs njengomba yophuhliso

Xa sikwinqanaba lokuqala lophuhliso loluntu neemfuno zabantu ndinyanzelwe imfuneko alunawo - .. Ingxowa yengqolowa, ababini ibhegi ingqolowa, njl Ukuze wenze oku, ukuba amanani zendalo, iiseti yinto ulandelelwano engenamda of integers N. HIV

Kamva, uphuhliso imathematika njengendlela inzululwazi, kuyimfuneko endle ethile integers Z leyo - oko kuquka amaxabiso akhabanayo kunye zero. imbonakalo yakhe kwinqanaba ekhaya, ukuba nomsindo kuba yinto yokuba ingxelo yokuqala kwafuneka ukulungisa thile amatyala kunye nelahleko. Kwinqanaba yenzululwazi, amanani akhabayo zenze kube lula ukucombulula elula zibalo yomgama. Phakathi kwezinye izinto, ke ngoku ukuba umfanekiso inkqubo engenamsebenzi ukuququzelela, okt. A. Kwakukho ingongoma reference.

Inyathelo elilandelayo yaba into ebangela ukuba ufake iinombolo iqhezu, ekubeni inzululwazi na ukuma, ezintsha ezifunyaniswe ngakumbi nangakumbi ifuna isiseko senkolelo ngenxa yokukhula push entsha. Ngoko kwakukho intsimi yamanani nenengqiqo Q.

Ekugqibeleni, akusekho ukuhlangabezana neemfuno nengqiqo, kuba zonke izinto ezintsha zifuna sesa ekugwetyelweni. Kwakukho entsimini amanani yokwenene R, imisebenzi incommensurability Euclid ngayo izixa ezithile ngenxa irrationality yabo. Oko kukuthi, sezibalo yamandulo yamaGrike kubekwe inani kungekuphela nje rhoqo, kodwa njengoko inani abstract leyo luphawulwa umlinganiselo magnitudes incommensurable. Ngenxa yokuba kukho amanani yokwenene, 'sibona ukukhanya "iinqobo ezifana' pi" kunye "e", ngaphandle imathematika mihla bekungazi kwenzeka.

Le amatsha yokugqibela yaba inani leqela C. Yaphendula uthotho lwemibuzo kunye umohlwayileyo postulates oyingenise kokudlulileyo. Ngenxa luphuhliso olukhawulezayo algebra Isiphumo enokuxelwa - ngamanani yokwenene, isigqibo iingxaki ezininzi akwenzeki. Umzekelo, enkosi amanani ezintsonkothileyo wema phandle theory umtya chaos eyandisiweyo kwizibalo ze hydrodynamics.

Misela Theory. cantor

Ingcamango Infinity ebesoloko yabangela impikiswano, njengoko kwakungenakwenzeka ukuba ukungqinelana okanye ukuchasa. Kwimeko yemathematika, nolusebenza postulates zingqinwe ngqo, ebonakalisa ngokwayo kakhulu ngokucacileyo, ngakumbi ukuba lo mba ubufundisi nangoku ubekwe kwinzululwazi.

Noko ke, ngenxa umsebenzi yezibalo Georg Cantor lonke ixesha kwaqinisekiswa. Ungqinile ukuba iiseti engenasiphelo kukho iseti ongapheliyo, nokuba intsimi R lingaphezulu intsimi N, makhe bobabini yaye nasiphelo. Phakathi kwinkulungwane XIX, iingcamango zakhe obala ububhanxa kunye ulwaphulo-mthetho nxamnye izimiso classical akaguquki, kodwa ixesha liya kubeka yonke endaweni yayo.

iimpawu Basic zasendle R

amanani Eyona kuphela ukuba iimpawu ezifanayo njengoko podmozhestva ukuba zibandakanya, kodwa leli ngamanye masshabnosti ngenxa sezulu:

• Zero R. ukhona kwaye lol endle c + = c 0 na c of R.
• Zero ukhona kwaye lol ukuba R. endle c x 0 = 0 na c of R.
• Umlinganiselo c: d xa d ≠ 0 likhona kwaye isemthethweni nayiphi c, d ka R.
• Field R wayalela, ngamanye amazwi xa c ≤ d, d ≤ c, ngoko c = d nayiphi c, d ka R.
• Ukudibanisa kwintsimi R aluguquki, ngamanye c + d = d + c, ngenxa yaso nasiphi na c, d ka R.
• Multiplication kwintsimi R aluguquki, ngamanye x c x d = d c bonke c, d ka R.
• Ukudibanisa kwintsimi R associative ngamanye (c + d) + f = c + (d + f) nawuphi na c, d, f of R.
• Multiplication kwintsimi R associative ngamanye (c x d) x f = c x (d x f) nawuphi na c, d, f of R.
• Ngokuba inani ngalinye yentsimi R malunga kuwo apho, kangangokuba c + (-c) = 0, apho c, -c evela R.
• Ngamnye inani yentsimi R ukho ludweliso wayo, kangangokuba c x c ^-1 = 1 apho c, c ^-1 ka R.
• Unit ukhona kwaye lol R, ukuze c x 1 = c, ngazo naziphi na c of R.
• It has unikezelo umthetho amandla, ukuze c x (d + f) = c x d + c x f, ngenxa yaso nasiphi na c, d, f of R.
• Intsimi R ngu zero akalingani umanyano.
• Field R ukusuka ': Ukuba c ≤ d, d ≤ f, ngoko c ≤ f nayiphi c, d, f of R.
• Xa umyalelo R kunye Ngaphezulu amaqhina oqhagamshelwano: Ukuba c ≤ d, ngoko c + f ≤ d + f bonke c, d, f of R.
• Xa umyalelo R kunye phindo edityaniswe: Ukuba 0 ≤ c, 0 ≤ d, ngoko 0 ≤ c x d nayiphi c, d ka R.
• Njengoko ezimbi nezilungileyo amanani wokwenene ngokuqhubekayo, ngamanye amazwi, ngenxa yaso nasiphi na c, d of R f, kukho evela R, ukuba c ≤ f ≤ d.

ifildi Module R

Amanani real ziquka into efana umnqongo. Yamiswa njengoko | f | nasiphi na f in R. | f | = F, ukuba 0 ≤ f kunye | f | = -f, ukuba 0> f. Ukuba sicinga umnqongo njengexabiso zejometri, oko umgama - akunamsebenzi, "badlula" wena zero kwi negative ukuya ezintle okanye phambili.

amanani Complex kwaye ibe yinyani. Zeziphi izinto ezifanayo nezahlukileyo?

By kunye namanani amakhulu, ezintsonkothileyo real - ke enye kwaye ziyafana, ngaphandle ukuba batshatiswe icandelo wengqikelelo i, kwisikweri apho ilingana no -1. Elements Fields R kunye C angamelwa le ndlela ilandelayo:

• c = d + f x i, apho d, f zezikaYe- endle R, kwaye i - unit ngengqondo.

Ukuze ufumane c of R f kulo mzekelo nje ekucingelwa ukuba nothi, oko kukuthi, akukho kuphela inxalenye yokwenene inani. Ngenxa entsimini amanani esimbaxa lo msebenzi ifanayo njengoko intsimi bokwenyani, f x i = 0 ukuba f = 0.

Ngokumalunga umahluko ezibonakalayo, umzekelo entsimini R quadratic equation ayikwazi ukuba kusonjululwe ukuba discriminant lelikhabayo, ngoxa ibhokisi C akuthethi iwise lo umda ngokubonisa iyunithi ezingqondweni i.

iziphumo

"Izitena 'of elikuwo kwaye postulates kuyo kwi kwisiseko zemathematika, musa ukutshintsha. On abanye babo ngenxa yokwanda kolwazi kunye nokwaziswa iingcamango ezintsha wabeka "izitena 'elandelayo, nto leyo kwixesha elizayo libe isiseko inyathelo elilandelayo. Umzekelo, amanani zendalo, nangona ukuba elucwangciso olusezantsi lwe the real intsimi R, angalahlekelwa ukufaneleka kwayo. Oko kubo sisiseko zonke izibalo samabanga aphantsi, oqalisa kukwazi yindoda yoxolo.

Ukusuka kwindawo ezenziwayo, amanani wokwenene ekhangeleka umgca othe ngqo. Kuyenzeka ukuba ukhethe indlela, ukuze ukuchonga imvelaphi kunye kwelizwi. Direct iquka inani engenasiphelo lamanqaku, nganye lihambisana inani lokwenyani enye, kungakhathaliseki nokuba ngaba kusengqiqweni. Ukusuka inkcazelo kucacile ukuba sithetha ingqiqo, leyo bezibalo jikelele isekelwe, kwaye ukuxhomekeka kolungiso ngokukodwa.