Trancendental number

A transcendental number is a real or complex number which is not algebraic -- not a solution of a non-zero polynomial equation with integer coefficients.

The most prominent examples of transcendental numbers are pi and e.

Proving that a given number is transcendental can be extremely difficult. However, transcendental numbers are not rare: almost all real and complex numbers are transcendental, since the algebraic numbers are countable, but the sets of real and complex numbers are uncountable.