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Transcendental number (view source)
Revision as of 00:52, December 29, 2007
, 00:52, December 29, 2007I added some more details
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]]'''''.
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>.
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]]