Examples
- The square root of 2 is algebraic over Q, since it is the root of the polynomial g(x) = x2 - 2 whose coefficients are rational.
- Pi is transcendental over Q but algebraic over the field of real numbers R: it is the root of g(x) = x - π, whose coefficients (1 and -π) are both real, but not of any polynomial with only rational coefficients. (The definition of the term transcendental number uses C/Q, not C/R.)
Read more about this topic: Algebraic Element
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