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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 <math>2</math>, <math>1/3</math>, 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 <math>e</math> and <math>\pi</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 <math>\pi</math>.

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]].