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Algebraic number

An algebraic number is a root of an equation in the form

in which the coefficients a0a1, ... an are all integers.



1. All rational numbers are algebraic because the fraction a / b is a solution of bx – a = 0.
2. The irrational number √2 is algebraic because it is a solution of x2 − 2 = 0.
3. The imaginary unit i is algebraic, as it is a root of x 2 + 1 = 0.


Additional information

If a real number or a complex number is not algebraic, it is called a transcendental number.

The algebraic numbers are countable as the number of polynomials with integer coefficients (and the number of roots per polynomial) are countable.


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