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algebraic number
A real number that is a root of a polynomial equation with integer coefficients. For example, any rational number a/b, where a and b are non-zero integers, is an algebraic number of degree one, because it is a root of the linear equation bx - a = 0. The square root of two is an algebraic number of degree two because it is a root of the quadratic equation x2 - 2 = 0. If a real number is not algebraic, then it is a transcendental number. Almost all real numbers are transcendental because, whereas the set of algebraic numbers is countably infinite, the set of transcendental numbers is uncountably infinite (see infinity).
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