Question: what is the difference between irrational and transcendental numbers?
Answer: A number x is irrational if it is not the solution of any algebraic equation of the first degree with integer coefficients, such as ax+b=0. A number z is transcendental if it is not the solution of any polynomial equation with integer coefficients of any degree n, such as a z^n+b z^(n-1)+ c z^(n-2)… +u z + v =0.