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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, [[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>.

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 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]].

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]]