Amanani a-rational

Kwi mathematika, irational number lilo naliphi na inani elinokubizwa ngokuba yiquotient okanye yifraction p/q yee integer ezimbini, up no q, libe linedenominator engu-q engalinganiyo no-zero.^[1] kuba ke u-q esenokulingana no- 1, yonke i-integer iba linani eli-rational. Ingqokolela yawo onke amanani a-rational ihlala ibonakalisa ngobhalo ongqindilili u Q (okanye umbhalo obhalwe ngqindilili kwibhodi emnyama ${\displaystyle \mathbb {Q} }$, i-Unicode iThemplethi:Unicode);^[2] wamiselwa ngo-1895 nguPeano emva kwe quoziente, igama lesiTaliyane elithetha i"quotient".

I- decimal expression ye-rational number isoloko inokuphelelwa emva kwenani lokugqibela kuludwe lwamanani okanye iqalise ukuphinda-phinda kwa olo ludwe lolandelelwano kwinani lokugqibela loo nto isenzeka ngokuya isenzeka ngokuphundaphindeneyo. Ngaphezu koko, naluphi na uphinda-phindo okanye ukupheliswa kwe-decimal kumele inani eli-rational. Ezi zivakalisi ziyinyaniso, kodwa zingeyonyaniso yebase 10 kuphela, kodwa zikwayinyaniso yayo nayohi na enye i-integer base (umzekelo ibinary, ihexadecimal).

I real number engekho rational ibizwa ngokuba yi-irrational. Amanani azii-iIrrational aquka [[izi-quare root zika 2|iThemplethi:Sqrt]], π, e, kunye neφ. I-decimal expansion yenani eli-irrational iyaqhuba ingaphindwa-phindwanga. Kuba ingqokolela yamanani a- rational numbers ikwazi ukubaleka countable, ibe yona ingqokolela yamanani angawo (iireal numbers) ingenakho ukuba ingabalwa, phantse onke ii-real numbers zi-irrational.^[1]

1. ↑ ^{1.0 1.1} Rosen, Kenneth (2007) Discrete Mathematics and its Applications (6th ed.) New York, NY: McGraw-Hill pp. 105,158–160 ISBN 978-0-07-288008-3 
2. ↑ Rouse, Margaret "Mathematical Symbols" retrieved 1 April 2015