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...umber''' is a [[complex number]] that is a root of a [[polynomial]] with [[rational number|rational]] coefficients. * Rational numbers are algebraic and of degree <math>\ 1.</math>&nbsp; The rational number ''a'' has defining polynomial <math> x-a </math>. All non-rational algebrai

{{r|Rational number}}

''zero'' is an integer, a rational number (the fraction 0/1),

...lve only small class of cubic equations, namely, those with at least one [[rational number|rational]] root. For such equations, all roots can be found by [[factor|fa

When dealing with <math>\mathbb{Q}</math>, the set of [[rational number]]s, we notice several things:

{{r|Rational number}}

{{r|Rational number}}

{{r|Rational number}}

Many common number systems, such as the [[integer]]s, the [[rational number]]s, the [[real number]]s, and the [[complex number]]s are abelian groups wi

...i.e. it is not solution of any [[polynomial]] having a finite number of [[rational number|rational]] coefficients.

{{r|Rational number}}

The minimal poynomial of an [[algebraic number]] α is the [[rational number|rational]] [[polynomial]] of least [[degree of a polynomial|degree]] which

...not matter that &mdash; because the fractions are not reduced &mdash; each rational number appears infinitely often.

...not matter that &mdash; because the fractions are not reduced &mdash; each rational number appears infinitely often.

.... In this article we treat quadratic extensions of the field '''Q''' of [[rational number]]s. ...is of the form <math>\mathbf{Q}(\sqrt d)</math> for a non-zero non-square rational number ''d''. Multiplying by a square integer, we may assume that ''d'' is in fac

...to zero. By division the set of integral numbers is augmented with the [[rational number]]s (quotients of two integral numbers).

...tive operations are [[addition]] and [[multiplication]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In this context associat

Value <math>\ g(x)</math>&nbsp; is a rational number whenever ''x'' is rational. For instance, for ''x'' = &frac12;:

* The [[rational number]]s as a [[subspace]] of the [[real number]]s with the Euclidean metric topo

* The [[rational number]]s form an ordered field in a unique way.