Difference between revisions of "Algebraic numbers"
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'''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>. | '''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 | + | 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]]). |
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]]. | 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]]. | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 04:16, December 29, 2007
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.