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An Algebraic Number is a number EQN:x which satisfies an algebraic equation i.e. an equation of the form

EQN:a_0x^n+a_1x^{n-1}+...+a_n=0

where

Real numbers which are not algebraic numbers are called transcendental numbers.

The size of the set of algebraic numbers is the size of countable sets EQN:\aleph_0.

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Exercise: By considering the