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Edit made on November 24, 2008 by DerekCouzens at 22:02:19

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HEADERS_END
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.

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Exercise: By considering the case equation EQN:ax+b=0 prove that all rational numbers are also algebraic numbers.