Nọ́mbà áljẹ́brà

(Àtúnjúwe láti Algebraic number)

Ninu mathematiiki, nomba aljebra je nomba tosoro kan to je wewe polynomial tikoje-odo ni oniyekiye eyo kan pelu oniipin (tabi lonibamu, odidi) afisodipupo. Awon nomba bi ${\displaystyle \pi }$ ti won ki se ti aljebra ni won so pe won je transcendental; Bi gbogbo won nomba gidi ni won je transcendental.

Àwọn àpẹrẹ

• Àwọn nọ́mbà gidi, tí wọ́n jẹ́ gbígbékàlẹ̀ bíi ìpín nọ́mbà odidi méjì a àti b, tí b kò dọ́gba mọ́ òdo, nitelorun ìtumọ̀ ọkè nítorí ${\displaystyle x=a/b}$ ni wẹ́wẹ́ ${\displaystyle bx-a}$.[1]
• Àwọn nọ́mbà ${\displaystyle \scriptstyle {\sqrt {2}}}$ àti ${\displaystyle \scriptstyle {\sqrt[{3}]{3}}/2}$ jẹ́ ti áljẹ́brà nítorípé àwọn ni wẹ́wẹ́ àwọn polynomials ${\displaystyle x^{2}-2}$ àti ${\displaystyle 8x^{3}-3}$, nitelentele.
• Ipin oniwura ${\displaystyle \phi }$ je ti aljebra nitoripe o je wewe kan polynomial ${\displaystyle x^{2}-x-1}$.
• Awon nomba kiko (those that, starting with a unit, can be constructed with straightedge and compass, e.g. the square root of 2) je ti aljebra.
• Awon quadratic surd (awon wewe quadratic polynomial ${\displaystyle ax^{2}+bx+c}$ pelu awon odidi afisodipupo ${\displaystyle a}$, ${\displaystyle b}$, ati ${\displaystyle c}$) je nomba onialjebra. Ti quadratic polynomial ba je monic ${\displaystyle (a=1)}$ nigbana awon wewe je quadratic integer.
• Awon nomba odidi Gauss: awon nomba tosoro ${\displaystyle a+bi}$ nibi ti ati ${\displaystyle a}$ ati ${\displaystyle b}$ je odidi na tun je quadratic integers.

Awon ini nomba aljebra

Fáìlì:Algebraicszoom.png
Algebraic numbers coloured by degree.
• Akojopo awon nomba aljebra je siseeka (enumerable).[3]
• Bi be, akojopo awon nomba aljebra ni iwon Lebesgue odo (gege bi akojopoabe fun awon nomba tosoro)

Itokasi

1. Some of the following examples come from Hardy and Wright 1972:159-160 and pp. 178-179
2. Also Liouville's theorem can be used to "produce as many examples of transcendentals numbers as we please," cf Hardy and Wright p. 161ff
3. Hardy and Wright 1972:160