An algebraic number is a number which is a root of some non-zero polynomial equation with rational coefficients.
A transcendental number is a number which is not a root of any non-zero polynomial equation with rational coefficients.
Are there any real numbers that are not the roots of any polynomial equation with algebraic coefficients?
I'm guessing that somebody must have asked this before somewhere, though I have not been able to find it, so please excuse me for the possible duplicate...
Thanks