Numerus algebraicus

Numeri algebraici sunt numeri ${\displaystyle x\in \mathbb {R} }$, qui solutiones aequationum polynominalium

Systemata Numerica Mathematicae

Numeri Elementarii
Naturales ${\displaystyle \mathbb {N} }$ {0,1,2,3,...} sive {1,2,3,...} Primi ${\displaystyle \mathbb {P} }$ {2,3,5,7,11,...} Abundantes Amicabiles Compositi Defectivi Perfecti Sociabiles Integri ${\displaystyle \mathbb {Z} }$ {...,-2,-1,0,+1,+2,...} Pares {...,-2,0,+2,...} Impares {...,-3,-1,+1,+3,...} Rationales ${\displaystyle \mathbb {Q} }$ Reales ${\displaystyle \mathbb {R} }$ Irrationales Numerus pi ${\displaystyle \pi =3.14159265358979\ldots }$ Numerus Euleri ${\displaystyle e=2.718281828459045\ldots }$ Complexi ℂ Algebraici Transcendentes Numerus imaginarius ${\displaystyle i={\sqrt {-1}}}$ Quaterni ${\displaystyle \mathbb {H} }$ Octoni ${\displaystyle \mathbb {O} }$ Infinitas ${\displaystyle \infty }$
Variae radices
Radix binaria(2) Radix octalis(8) Radix decimalis(10) Radix sedecimalis(16)

${\displaystyle x^{n}+a_{n-1}\cdot x^{n-1}+\dots +a_{1}\cdot x+a_{0}=0,}$

${\displaystyle \ a_{i}\in \mathbb {Q} \ \forall i\in {\lbrace 0,\ldots ,n-1\rbrace }}$

sunt. Copia numerorum algebraicorum est corpus.

Exempla

• Omnes numeri ${\displaystyle q\in \mathbb {Q} }$ sunt algebraici, nam aequationem ${\displaystyle x-q=0}$ solvunt.
• ${\displaystyle {\sqrt {2}}}$ est numerus algebraicus, nam aequationem ${\displaystyle x^{2}-2=0\,}$ solvit.
• ${\displaystyle \pi }$ non est numerus algebraicus (id est: ${\displaystyle \pi }$ est numerus transcendens; ad demonstrationem videndam).