an irrational number that is not algebraic

an irrational number that is not a root of any polynomial equation with integer coefficients

a number but can't be expressed in any finite series of either arithmetical or algebraic operations

a number that can not be described by algebraic equations with rational coefficients

a number that isn't the root of any polynomial equation with integer coefficients

a (possibly complex) number that is not the root of any integer polynomial , meaning that it is not an algebraic number of any degree

In mathematics, transcendental means "non-algebraic", where an algebraic number is the solution of a non-zero polynomial equation with integer (or, equivalently, rational) coefficients. Thus a transcendental number is a (real, imaginary or complex) number which is not the solution of any such equation.