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'''Algebraic numbers''' are numbers which are roots of some finite degree [[polynomial]] with integer coefficients.  Examples of real algebraic numbers are 2, 1/3, and <math>\sqrt{2}</math>.

'''Algebraic numbers''' are numbers which are roots of some finite degree [[polynomial]] with integer coefficients.  Examples of real algebraic numbers are 2, 1/3, and <math>\sqrt{2}</math>, which are roots of the polynomials <math>x-2=0</math>, <math>3x-1=0</math>, <math>x^2-2=0</math>, respectively.

In contrast, [[transcendental numbers]] are 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> ([[pi]]), though this must be proven using advanced [[calculus]] or [[number theory]].

In contrast, [[transcendental numbers]] are 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> ([[pi]]), though this must be proven using advanced [[calculus]] or [[number theory]].