Algebraic number
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer coefficients. For example, the golden ratio, / 2, is an algebraic number, because it is a root of the polynomial x⁲ − x − 1. That is, it is a value for x for which the polynomial evaluates to zero. As another example, the complex number 1 + i is algebraic because it is a root of x⁴ + 4. All integers and rational numbers are algebraic, as are all roots of integers. Real and complex numbers that are not algebraic, such as π and e, are called transcendental numbers. The set of algebraic numbers is countably infinite and has measure zero in the Lebesgue measure as a subset of the uncountable complex numbers. In that sense, almost all complex numbers are transcendental.
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