Difference between revisions of "Algebraic numbers"
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| − | '''Algebraic | + | '''Algebraic numbers''', are real numbers which are roots of some finite degree polynomial with integer coefficients. Examples of Algebraic Numbers are 2, 1/3, and <math>\sqrt{2}</math>. |
In contrast, [[transcendental numbers]] are real numbers which are not roots of any finite degree polynomial with integer coefficients. The most well-known transcendental numbers are [[e]] and <math>\pi</math> ([[pi]]). | In contrast, [[transcendental numbers]] are real numbers which are not roots of any finite degree polynomial with integer coefficients. The most well-known transcendental numbers are [[e]] and <math>\pi</math> ([[pi]]). | ||
Revision as of 03:53, March 7, 2008
Algebraic numbers, are real numbers which are roots of some finite degree polynomial with integer coefficients. Examples of Algebraic Numbers are 2, 1/3, and .
In contrast, transcendental numbers are real numbers which are not roots of any finite degree polynomial with integer coefficients. The most well-known transcendental numbers are e and (pi).
The set of Algebraic Numbers is countably infinite. This follows from the fact that the set of finite degree polynomials with integer coefficients is countably infinite.