Ero sivun ”Algebrallinen luku” versioiden välillä

13 770 merkkiä lisätty ,  10 vuotta sitten
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p (r2.6.5) (Botti lisäsi: kk:Алгебралық сан)
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Yhtälöä nimitetään algebralliseksi, jos siinä <math>P(x)</math> on polynomi, jonka kertoimet ovat [[kokonaisluku]]ja (tai yhtäpitävästi [[rationaaliluku]]ja) ja ainakin yksi niistä on nollasta eroava.
Esimerkiksi luvun <math>2</math> neliöjuuren käänteisluku on algebrallinen, sillä se on algebrallisen yhtälön <math>2x^2-1=0</math> juuri. Myös [[Kompleksiluku|imaginaariyksikkö]] <math>i</math> on algebrallinen, sillä se toteuttaa yhtälön <math>x^2+1=0</math>. Jokainen rationaaliluku <math>x=m/n</math> (missä <math>m,n</math> ovat kokonaislukuja) on myös algebrallinen luku, koska se toteuttaa yhtälön <math>nx-m=0</math>.
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Algebrallisen luvun vastakohta on [[transkendenttiluku]]. Transkendenttisia ovat siis kaikki muut kompleksiluvut, ja ne eivät toteuta mitään algebrallista yhtälöä.
 
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