Algebraic number

English

Noun

1. Template:Lb 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.

   The golden ratio (φ) is an algebraic number since it is a solution of the quadratic equation $x^2+x-1=0$, whose coefficients are integers.

   The square root of a rational number, $\sqrt{\frac{m}{n}}$, is an algebraic number since it is a solution of the quadratic equation $n{x}^2-m=0$, whose coefficients are integers.

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   • 1991, Template:W, 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:

     (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).

Hyponyms

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Coordinate terms

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See also

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Further reading

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• Algebraic number on Template:W
• algebraic number on Template:W
• Algebraic Number on Template:W