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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 EQN:a_0,{\quad}a_1,{\quad}\ldots{\quad}a_n are integers, not all zero. 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. ---- Exercise: By considering the equation EQN:ax+b=0 prove that all rational numbers are also algebraic numbers.