Amanani angaqhelekanga kunye namanani asinceda sazi ukuba leliphi kuzo elinokwahlulahlula ngamanani amabini okanye elinye elinokwahlulwa ngamaqela amabini. Kodwa ukufunda okungakumbi malunga nala maxabiso, siyakumema ukuba uqhubeke nathi kweli nqaku.

amanani-angalinganiyo

Amanani angaqhelekanga kunye namanani

Xa uthetha ngamanani angaqhelekanga, indlela yokusombulula ukwahlulwa kwenani elinokwahlulwa kabini liboniswa, ekwalilo nani lilonke. Kwelinye icala, kuthiwa yahlulahlulwe ngamaqela amabini; Kwimathematika, iingxaki ezahlukeneyo zinokusonjululwa xa inani lahlulahlulwa ngamanani ukusuka ku-2.

Imisebenzi yenziwa ngokukhupha okanye ukongeza amanani ama-2 kwinani ukuze iqhezu ledesimali lingaveliswa. Umzekelo, inani u-10 linani elilinganayo ukusukela ulwahlula-hlula ngeziphumo ezi-2 kwinani eliphindaphindwe ngesi-2, isiphumo salo linani lokuqala u-10.

Inani kuthiwa alingaqhelekanga xa lingalinganiyo, ke aziziphinda-phindo zika-2. Xa amaxabiso ama-2 edityanisiwe, isiphumo esisenani elingaqhelekanga; Kukwathiwa inani elingaqhelekanga lelona, ​​nokuba lililo, longeza inani u-1 kwaye ixabiso lifunyenwe linjalo, masibone lo mzekelo M = 2 xn + 1, apho M linani elingaqhelekanga no "n" naliphi na inani.

Kukwakho noqikelelo oluthi inani elipheleleyo elingadibananga, kodwa liphindaphindwe ngo-2, lithathwa njengenani elingaqhelekanga; ke, ungadibanisa okanye uthabathe isi-2 kwelo nani lingaqhelekanga, ufumane elinye nelinye inani. I-axiom yemathematika ithi oku kulandelayo:

Msgstr "Inani elipheleleyo lingaqhelekanga xa kukho enye inani elipheleleyo"

Iifomula zamanani amanani

Kukho iifomula eziphambili zokuvelisa amanani, akhiwa ngokudala ukuphindaphindwa kwesi-2 kunye neenombolo zendalo ezikhethwe ngokungahleliwe. Oku kunokuba zezi zilandelayo: 0 + 2 = 2, 2 + 2 = 4, 2 + 2 + 2 = 6, 2 + 2 + 2 + 2 = 8 njalo njalo de kube kufikelela kumaxabiso anokufikelela infinito.

La maxabiso akhokelela kwixabiso elifanayo, xa ukuphinda-phinda kusetyenziswa masibone: 2 × 1 = 2, 2 × 2 = 4, 2 × 3 = 6, 2 × 4 = 8. Ngendlela efanayo, banokwandiswa bafike kwelona nani likhulu silifunayo; Uluhlu olulandelelanayo lwamanani lwenziwe ukusuka kwinombolo yesi-2, ukusukela ngoko ukuya ku-2 kongezwa okanye kongezwa kwinani elilandelayo kwaye ngokulandelelana, onke amanani afunyenwe.

Ifomula yokuvelisa la manani ngaphandle kwesidingo sokwandisa uluhlu yile ilandelayo P = 2n, apho (n) kukho naliphi na inani lendalo. Ngenxa yoko, uthotho lwamanani apheleleyo anokuveliswa ukusuka ku-minus infinity ukuya ku-infinity.

Iifomula zamanani amnqakathi

Sele siyazi ukuba inani elingaqhelekanga linani elilinganayo nelidityaniswa ngo-1 Ngale ndlela singasombulula ingxaki; kodwa ngokwembono yezibalo, indlela yokuyilwa kwayo iya kuba yile ilandelayo: I = 2n + 1, esele ibonwe ngaphambili, apho (n) kukho naliphi na inani lendalo.

Ngale ndlela ifomula yenziwa kuthotho, ukuqala ku-0; 2 (0) + 1 = 1, emva koko 2 (1) + 1 = 3, 2 (2) + 1 = 5, 2 (3) +1 = 7, njengoko sibona ixabiso «n» esilabela lona ifomula uthotho lwamanani alandelelanayo aqala ku "0" kwaye sifumana inani lamanani angaqhelekanga, ukongeza naliphi na inani elinokufikelela kubunzulu.

Iimpawu kunye neempawu

Elinye lala manani lineepropathi ekufuneka zihlonitshwe yimithetho ethile yemathematics. Siza kuqala ngokuchaza enye enxulumene namanani, ekulula ukuwasebenzisa ekusebenzeni, kuba ukwahlula ngo-2, iinkqubo zihlala ziba nobuhlobo.

Kwamanani nkqu

Singaqala ngokuthi enye yeepropathi zokuqala kukuba inemeko engapheliyo nokuba yeyamanani endalo okanye amanani apheleleyo (…… 2, -2, 4, -4, 8, -6,…).

Ngendlela efanayo, kwanamanani aqulathe izinto ezifanayo namanani endalo. Ukuphindaphindwa kwamabini ama-2 kwenza ukuqhubela phambili kwe-arithmetic kunye nemeko efanelekileyo yenombolo 2 kunye nokusebenzisa u-0 njengekota yokuqala; Kwangokunjalo, umlinganiso weseti yamanani endalo ikwaluseti lwamanani endalo angaqhelekanga, nangona engadibananga, amanyene ngokudibana kwawo namanani eN (endalo).

Nditsho amanani anenani elinye nelona lide, eli linani lesi-2: amanye amanani amanani adityanisiweyo kuba evuma abahluli ababini. Kwangokunjalo, iseti ye «N» kwizibini ezi-odolweyo kunye nobudlelwane obungaphantsi kwe-0 (<), apho elo nani limele ubuncinci kunye nenani lokuqala.

Enye ipropathi ebalulekileyo yamanani kukuba ukongeza okanye ukuthabatha amanani amabini endalo kunye nenani lamandla kunye nomboniso ngaphandle kwe-0 uhlala ekhokelela kwinani elifanayo. Kwelinye icala, i-quotient yamanani amabini (angabinabo umahluli be-0, nokuba ayiqhelekanga okanye engaqhelekanga), isiphumo sisoloko siyakuba linani elilinganayo.

Isikwere senani elilinganayo "N" lithathwa njengepropathi, likhokelela kwelinye inani. Ngenxa yoko, ingcambu yesuntswana lenani elilinganayo lelinye inani.

Kumanani angaqhelekanga

Iipropathi zamanani angaqhelekanga aneemeko ezithile ezinomdla kunye nobudlelwane. Umzekelo, uthotho olungaqhelekanga alunasiphelo, kuba luthotho olubhalwe kwi-odd, ukuze zonke izinto ezingaqhelekanga zilingane nenani elidityanisiweyo. Enye imeko yile ilandelayo, ikota yokuqala eyinombolo 1, ikwalinombolo yokuqala kuthotho lwamanani "N".

Isiqingatha sawo onke amanani "N" naphakathi kothixo ayiqhelekanga amanye aseleyo. Enye ipropathi ibonisa ukuba uthotho olungenasiphelo lwamanani aphambili (ngaphandle kweenombolo 2), lubandakanya uthotho olungathandabuzekiyo, oku kuthetha ukuba kungenjalo kuya kubakho amanani aphambili kuthotho lwee-messes zamanani.

Okokugqibela, kuhlala kukuhle ukuhlala unolwazi kunye nendlela apho amanani aphathwa ngayo kwimathematics. Abazali kufuneka bagxile kwimisebenzi enikezelwe kuyo amanani angaqhelekanga kunye namanani abantwana xa bethatha amanyathelo okuqala kwimfundo yamabanga aphantsi; nangona kunjalo ukuchonga kulula kakhulu, ngokwazi ukuba inani liphela ngo-2, kugqityiwe ukuba linani elilinganayo.

Funda ngakumbi ngala manani ngokufunda inqaku elilandelayo elihambelana nesi sihloko Athini amanani eDesimali?