Algebraic Number 

$a_0x^n+a_1x^{n1}+...+a_n=0$
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.