Yini ukuhlukaniswa kwezinombolo zangempela?

I-Los izinombolo zangempela yiyona iqoqo lezinombolo ezinengqondo nezingenangqondo ukwedlula okukhona, okungenzeka ukuthi uthole izinhlobo ezahlukahlukene zazo. Lezi zazalwa ngenxa yesidingo esatholakala phakathi nekhulu le-XV nele-XVII lapho ukubalwa kwakungeke kwenzeke ukuchazwa ngendlela enengqondo futhi enembile, okujwayele ukusetshenziswa kwamagama noma izinkulumo ezingathembekile, ezinjengokuthi "okuncane" noma "umkhawulo".

Yize abaseGibhithe bevele besebenzisa izingxenyana, bekungekho kuze kube sezibalo zamaGreki lapho "inombolo" yafundwa khona ngendlela yefilosofi, lapho abalandeli bakaPythagoras baphetha ngokuthi konke okubazungezile kuyizinombolo; ngakho-ke, lawa asetshenziswa ezindaweni ezahlukahlukene.

Ukuhlukaniswa kwezinombolo zangempela ngokohlobo lwazo

Lezi zinombolo zingahlukaniswa zibe yizinhlobo ezimbili, esishilo ekuqaleni, okungukuthi, izinombolo ezinengqondo (ezakhayo, ezingezinhle no-zero) nezingenangqondo (i-algebraic ne-transcendental). Ngokuqondile, kungenzeka ukuthola ukuhlukaniswa okulandelayo:

1. Izinombolo ezinengqondo

Izinombolo ezinekhono lokumelwa njengokuhlukaniswa kwezinombolo eziphelele, noma okufanayo, ingxenyenamba ejwayelekile neyamanje lapho isibalo nenani elincane kungabi zero noma ngaphansi kunalokho okubizwa ngale ndlela.

Lezi nazo zihlukaniswe zaba izinhlobo eziningana: izinombolo eziphelele (zemvelo, zero nezinombolo ezingezinhle) nezingxenyana (izingxenyana ezifanele nezingafanele).

a) Izinombolo eziphelele

Izinombolo ziqoqo lezinombolo zemvelo, izinombolo eziphikayo kanye no-zero, ezimelwe uhlamvu "Z" Izinombolo nazo zivame ukumelwa kulayini wezinombolo, lapho okuhle noma okungokwemvelo kungakwesokudla, uziro phakathi nophikisayo ngakwesobunxele.

• Kucatshangelwa "izinombolo zemvelo”Kulabo abasetshenziselwa ukubala izinto noma ukwenza eminye imisebenzi ejwayelekile futhi elula yokubala.
• El Cero Inani elize, okungukuthi, alinaso isibalo esibalulekile lapho lingahambisani. Kodwa-ke, isikhundla saso enombolweni singayiguqula ngokuphelele incazelo, ngoba lapho ingakwesokudla sayo lapho ingaphindaphinda inani ngeyishumi; ngenkathi ngakolunye uhlangothi kungekho ukuguqulwa.
• I-Los izinombolo ezingezinhle Zisetshenziswa ziphikisana nokuhle noma okwemvelo, okungukuthi, esikhundleni sokubala, ukusetshenziswa kwazo ukususa, ukweleta, ukuchitha noma ukuba ngaphansi. Ukubalula kuyadingeka ukuthi kuboniswe igama elithi "minus" ngaphambi kwenombolo, isibonelo "minus four".

b) Ukuhlukaniswa

Futhi ngaphakathi kwezinombolo zangempela kungenzeka ukuthola lolu hlobo kuzilinganiso, ezaqala ngenhloso ye- ukuxazulula izinkinga maqondana nokwahlukaniswa kwezinombolo zemvelo. Inombolo yamaqhezu imane nje iyinkulumo ekhombisa ukuhlukaniswa kwenani elilodwa ngenye.

Izingxenyana zibonakala ngokuba nenombolo nezinombolo, ezihlukanisiwe ngomugqa ohlukanisayo noma ovundlile. Kodwa-ke, ngaphandle kokuthi kuma-integer singathola futhi "ingxenyenamba elula", kulesi sigaba izinhlobo zezingxenyana esithola ukuthi zilungile futhi azilungile.

• Ezifanele ziqukethe lezo lapho i-numerator ingaphansi kune-denominator.
• Okungafanelekile kungaba okuphambene, okungukuthi, i-denominator inkulu kune-denominator.

2. Izinombolo ezingenangqondo

Ama-Irrationals yilezo zinombolo ezingenalo ikhono lokubhalwa ngocezu, ngoba amadesimali abo aqhubeka nokuziphinda ngokungenamkhawulo. Isibonelo, akunakwenzeka ukubhala ingxenyenamba efaka i- inombolo Pi, e, isilinganiso segolide nezimpande isikwele, i-cubic, phakathi kwabanye.

Izinombolo ezingenangqondo zavela ngenxa yesidingo sokuba umfundi wasePythagoras abhale impande njengengxenyana; ukubona ukuthi lokhu akunakwenzeka nokuthi kwakuyinombolo esiyaziyo namuhla ngaphansi kwegama "elingenangqondo". Kodwa-ke, uPythagoras akavumelananga nokutholakala kwakhe, yize kuthiwa kubhekiswe kuye njengesikole sakhe.

Ngaphezu kwalokho, lezi zingahlukaniswa zibe izinhlobo ezimbili, i-algebraic ne-transcendental.

• I-Los i-algebraic yilawo avumela ukuxazululwa kwesibalo se-algebraic.
• I-Los edlulele Yilezo ezingenakumelwa inani elilinganiselwe lezimpande (ngokungafani ne-algebraic) futhi ezingalandeli iphethini kuma-decimals abo. Phakathi kwabo sithola inombolo uPi.

Kuze kube manje siza ngokuhlukaniswa kwezinombolo zangempela, esinethemba lokuthi kube lula ukuzifunda nokuziqonda; njengoba abantu abaningi bengabathandi bezibalo futhi senze konke okusemandleni ethu ukunikeza incazelo enemininingwane nelula.