Difference between revisions of "Transcendental number"
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PhineasBogg (talk | contribs) m (I added some more details) |
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| − | A '''transcendental number''' is a real or complex [[number]] that is not algebraic; i.e. is not a solution of a polynomial equation with integer coefficients. | + | 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]]'''''. | Some famous examples of transcendental numbers include '''''π''''' ([[pi]]) and '''''[[e]]'''''. | ||
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| + | In contrast, [Algebraic Numbers], are real numbers which are roots of some finite degree polynomial with integer coefficients. Examples of Algebraic Numbers are <math>2</math>, <math>1/3</math>, and <math>\sqrt{2}</math>. | ||
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| + | 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]] | ||
Revision as of 00:52, 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 , , 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.