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

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

where $a_0,{\quad}a_1,{\quad}\ldots{\quad}a_n$ 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 $\aleph_0.$

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

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