Lambarada Real iyo xoolahoodii,

Baytagooris sheegtay in tirada waa aasaaska dunida on par leh walxaha waaweyn. Plato rumeysan yahay in tirada links arrin iyo noumenon ah, ka caawiyay in ay ogaadaan, in la miisaamay iyo in gebagebo. Xisaabta ka timaadaa ereyga "arifmos" - tirada, Bar bilaw in xisaabta. Waxaa suurto gal ah in lagu qeexo wax kasta - laga bilaabo dugsiga hoose ilaa tufaax meelaha aan la taaban karin.

Baahiyaha sida factor horumarinta ah

In marxaladaha hore ee horumarinta bulshada baahida dadka oggolaysiiyeen by baahida loo qabo in ay sii score - .. Mid ka mid ah bac oo ah hadhuudh, laba bac hadhuudh, iwm Si arrintan loo sameeyo, waxaa loo tirooyinka caadiga ah, set dhan yahay xigxiga ah aan la koobi karayn abyooneyaasha N. wanaagsan

Later, horumarinta xisaabta sida sayniska, waxa ay ahayd lagama maarmaan in beerta gaarka ah ee abyoonayaasha Z - waxaa ka mid ah qiimaha negative iyo eber. Saftay heerka qoyska, waxaa kacay by xaqiiqada ah in xisaabaadka hore u lahaa in ay bartey hagaajin ah daymaha iyo khasaare. On heer sayniska, tirooyinka taban ayaa ka dhigtay in ay suurto gal ah si ay u xalliyaan fudud isleegyo qumman. Waxyaabaha kale, hadda waa suurto gal ah in image nidaam Ciyaalle duwo, ie. A. Waxaa jiray dhibic ka mid ah tixraac.

Tallaabada xigta ahaa baahida loo qabo in ay galaan tiro jajab, tan iyo sayniska uusan weli ma taagnaan, ikhtiraac cusub iyo aad u badan dalbaday in si joogto ah afka baarkiisa koritaanka a riix cusub. Sidaas daraaddeed waxaa ku beer tirooyinka buuxa Q.

Ugu dambeyntii, mar dambe ma la kulmaan baahida ugu macquulsan, sababtoo ah dhammaan natiijooyinka cusub waxay u baahan yihiin inay xaq ka dhigto. Waxaa jiray beer lambarada R dhabta ah, shuqullada Euclid ee incommensurability of tiro gaar ah sababtoo ah irrationality. Taasi waa, xisaabyahan Greek qadiimiga u taagan tiro ma aha oo kaliya sida joogta ah, laakiin sida qiimaha ah aan la taaban karin, taas oo ah waxa lagu gartaa ratio ee cabirkiisu incommensurable. Sababo la xaqiiqada ah in ay jiraan tiro dhab ah, "waxaan ku arkay iftiinkii" qiyamka sida "pi" iyo "e", iyada oo aan taas xisaabta casriga ah ma qaadi karo meel.

cusub ee final ahayd tiro adag C. Waxa jawaabay su'aalo taxane ah oo beeniyay postulates hore galay. Sababo la horumarinta degdegga ah ee natiijada algebra ahaa saadaalin karo - iyadoo tirada dhabta ah, go'aanka dhibaatooyin badan oo aan suurto gal ahayd. Tusaale ahaan, in tirada adag mahad istaagay baxay aragti string iyo fowdo balaariyay isleegyo of hydrodynamics.

Calan Aragtida. pappi

Fikradda ah xad la'aan ayaa had iyo jeer keena muran, maadaama ay ahayd wax aan macquul aheyn inay caddeeyaan ama diidaan. In macnaha guud ee xisaabta, kaas oo ku shaqeeya postulates adag xaqiijin, isu muujiyey ugu cad, ayaa in ka badan in arrin fiqi ahaaneed weli miisaamay sayniska.

Si kastaba ha ahaatee, iyada oo loo marayo shaqo ee xisaab Georg Cantor wakhtiga oo dhan ka dhacday meel. Waxa uu cadeeyay in nooc aan la koobi karayn jiro set ah aan la koobi karayn, iyo in R beerta ka wada weyn yahay N berrinka, oo labadoodaba waxaa ka ha iyo ma idlaan. In dhexe ee qarnigii XIX, iyo fikradaha uu si cad u yeedhay micne lahayn iyo dambi ka dhan ah Buzadag aan beddelmi karin classical, laakiin mar walba in ay meel gelin doonaa.

guryaha aasaasiga ah ee R berrinka

tirada dhabta ah oo kaliya ma laha sifooyinka la mid ah sida podmozhestva in ay ka mid ah, laakiin waxaa kaabaya masshabnosti kale by Samo falku inaad ah xubno ay:

• Zero R. jirta iyo iska leh beerta c ah + = c 0 for c mid ka mid ah R.
• Zero jirta iyo iska R. beerta c x 0 = 0 for c mid ka mid ah R.
• c ratio The: d markii d ≠ 0 jirta iyo shaqeynayaa wixii c, d ee R.
• Field R amartay, i.e. haddii ≤ c d, d ≤ c, ka dibna c = d wixii c, d ee R.
• Intaa waxaa dheer in R beerta waa hormagalinta, i.e. c + d = d + c, wixii c, d ee R.
• Isku dhufashada in R beerta waa hormagalinta, i.e. x c x d = d c for dhan c, d ee R.
• Intaa waxaa dheer in R beerta waa israacinayo i.e. (c + d) + f = c + (d + f) wixii c, d, f ee R.
• Isku dhufashada in R beerta waa israacinayo i.e. (c x d) x f = c x (x d f) wixii c, d, f ee R.
• Waayo, tiro kasta oo duurka R soo horjeeda in ay halkaas, sida in c + (-C) = 0, halkaasoo c, -C ka R.
• Waayo, tiro kasta oo ka mid R beerta jirta ay bedelka, sida in c x c ^-1 = 1 meesha c, c ^-1 ee R.
• Unit jirta iyo iska R, si c x 1 = c, waayo c mid ka mid ah R.
• Waxay leedahay qaybinta sharciga awoodda, si c x (d + f) = c x d + x c f, wixii c, d, f ee R.
• beerta R waa eber ma qummana in midnimada.
• Field R waa transitive: haddii ≤ c d, d ≤ f, ka dibna c ≤ f wixii c, d, f ee R.
• In R oo intaas dheer si yihiin isku xidhan, haddii ≤ c d, ka dibna c + ≤ f d + f ee dhammaan c, d, f ee R.
• Si ee R iyo isku dhufashada lala: haddii 0 ≤ c, 0 ≤ d, ka dibna 0 ≤ c x d wixii c, d ee R.
• Sida tirada dhabta ah negative iyo positive waa joogto, i.e., wixii c, d of R f, waxaa laga R, c in ≤ f ≤ d jira.

beerta Module R

Tirada dhabta ah waxaa ka mid ah wax sida module ah sida. waxa loo qoondeeyey sida | f | waayo, f kasta R. | f | = F, haddii 0 ≤ f iyo | f | = -f, haddii 0> f. Haddii aan ka fiirsan module sida qiimaha joomateri, waa meel fog - ma laha, "maray" aad sida eber ee xun si fiican ama weerarka.

lambarada Complex iyo dhabta ah. Maxay yihiin egyihiin iyo khilaafaadka?

By iyo tiro badan, adag oo dhab ah - ay tahay mid ka mid ah oo la mid ah, marka laga reebo in marka hore ay i soo biiray unugga khayaali ah, square ah kuwaas oo waa loo siman yahay si -1. Qaybaha beeraha R iyo C matali karaan by formula soo socda:

• c = d + f x i, kuna waari dhexdeeda d, f ka tirsan R berrinka, iyo i - unit khayaali ah.

Si aad u hesho c ee R f kiiskan si fudud u qaataa inay tahay eber, ie, waxaa jira kaliya ay qeyb ka dhabta ah ee tirada. Maxaa yeelay, berrinkii tirada adag ayaa feature isla dhigay sidii beer ee dhabta ah, f x i = 0 haddii f = 0.

Iyada oo la eego kala duwanaanshaha la taaban karo, tusaale ahaan duurka R ka isla'egta saablay aan lagu xallin karaa haddii discriminant uu yahay diidmo, halka sanduuqa C uusan soo rogi xaddidaadda this by bandhigid unugga khayaali ah i.

natiijooyinka

"Lebenkii" ee axioms iyo postulates on taas oo ay u xisaabta saldhig, ma beddeli. On qaar iyaga ka mid ah ay sabab u tahay kororka macluumaadka iyo hordhaca ah ee aragtiyaha cusub kaalinta ku "lebenkii" soo socda, taas oo mustaqbalka noqon karaan aasaas u ah tallaabada xigta. Tusaale ahaan, tirooyinka caadiga ah, inkastoo xaqiiqda ah in ay yihiin hoosaad ka mid ah R dhabta ah ee beerta, ma lumin ay ku tacaluqa. Waa iyaga ku salaysan xisaabinta hoose oo dhan, taas oo ka bilaabanayso aqoonta nin nabadda.

Laga soo bilaabo dhibic la taaban karo of view, tirada dhabta ah u eg xariiq toosan. Waxaa suurto gal ah in aad doorato jihada a, si ay u aqoonsadaan ka soo jeedo iyo garoonka. Direct ka kooban tiro aan la koobi karayn of dhibcood, kuwaasoo mid walba uu u dhigantaa tiro ka mid ah hal dhabta ah, iyadoo aan loo eegin ama aan caqligal ah. From sharaxaad waxaa cad in aan ka hadlayno fikradda, kaas oo ku salaysan yahay xisaabta guud ahaan, iyo falanqaynta xisaabeed gaar ahaan.