Dictionary

algebraic number en · NOUN

Meanings

1. A complex number (more generally, an element of a number field) that is a root of a polynomial whose coefficients are integers; equivalently, a complex number (or element of a number field) that is a root of a monic polynomial whose coefficients are rational numbers.
   • Thus, the equation x-eʸ#61;0 is satisfied for x#61;1,#92;y#61;0 and for no other pair of algebraic numbers. 1918, The American Mathematical Monthly, volume 25, Mathematical Association of America, page 435:
   • (i) It is easily checked that the set of all algebraic numbers is countable, whereas the set of all complex numbers is uncountable (this non-constructive proof goes back to Cantor). 1991, P. M. Cohn, Algebraic Numbers and Algebraic Functions, Chapman & Hall, page 83, The existence of such 'transcendental' numbers is well known and it can be proved at three levels
   • As a matter of fact, it is not true that the algebraic numbers above can be factored uniquely, but the first case of failure occurs when p = 23. 1921, L. J. Mordell, Three Lectures on Fermat's Last Theorem, page 16:
   • The square root of a rational number, √, is an algebraic number since it is a solution of the quadratic equation nx²-m=0, whose coefficients are integers.
   • The golden ratio (φ) is an algebraic number since it is a solution of the quadratic equation x²-x-1=0, whose coefficients are integers.

Forms

Coordinates

transcendental number

Deriveds

algebraic number theory

Hyponyms

algebraic integer · phi · golden ratio

Relateds

algebraic integer

Translations (20)

hu algebrai szám (element of a number field that is a root of a polynomial with integer coefficients) · sh algebarski broj (element of a number field that is a root of a polynomial with integer coefficients) · sv algebraiskt tal (element of a number field that is a root of a polynomial with integer coefficients) · la numerus algebraicus (element of a number field that is a root of a polynomial with integer coefficients) · ro număr algebric (element of a number field that is a root of a polynomial with integer coefficients) · cs algebraické číslo (element of a number field that is a root of a polynomial with integer coefficients) · gl número alxébrico (element of a number field that is a root of a polynomial with integer coefficients) · ko 대수적 수 (element of a number field that is a root of a polynomial with integer coefficients) · is algebrutala (element of a number field that is a root of a polynomial with integer coefficients) · is algebruleg tala (element of a number field that is a root of a polynomial with integer coefficients) · fi algebrallinen luku (element of a number field that is a root of a polynomial with integer coefficients) · ru алгебраическое число (element of a number field that is a root of a polynomial with integer coefficients) · cmn 代數數 /代数数 (element of a number field that is a root of a polynomial with integer coefficients) · th จำนวนเชิงพีชคณิต (element of a number field that is a root of a polynomial with integer coefficients) · fr nombre algébrique (element of a number field that is a root of a polynomial with integer coefficients) · de algebraische Zahl (element of a number field that is a root of a polynomial with integer coefficients) · kk алгебралық сан (element of a number field that is a root of a polynomial with integer coefficients) · tr cebirsel sayılar (element of a number field that is a root of a polynomial with integer coefficients) · pl liczba algebraiczna (element of a number field that is a root of a polynomial with integer coefficients) · it numero algebrico (element of a number field that is a root of a polynomial with integer coefficients)