Difference between revisions of "Transcendental number"
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Some famous examples of transcendental numbers include '''''π''''' ([[pi]]) and '''''[[e]]'''''. | Some famous examples of transcendental numbers include '''''π''''' ([[pi]]) and '''''[[e]]'''''. | ||
| − | In contrast, [[ | + | In contrast, [[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>. |
| − | The set of | + | The set of transcendental numbers is uncountably [[infinite]]. This follows from the facts that the set of real numbers is uncountably infinite and the set of algebraic numbers is countably [[infinite]]. |
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Latest revision as of 02:21, December 29, 2007
A transcendental number is a real or complex number that is not algebraic; i.e. is not a solution of a finite degree polynomial equation with integer coefficients.
Some famous examples of transcendental numbers include π (pi) and e.
In contrast, 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 .
The set of transcendental numbers is uncountably infinite. This follows from the facts that the set of real numbers is uncountably infinite and the set of algebraic numbers is countably infinite.