I'm reading some basic introduction on fields and Galois theory.
By definition, let $F$ be an extension field of $K$ -- An element $u$ of $F$ is said to be algebraic over $K$ provided that $u$ is a root of some nonzero polynomial $f \in K[x]$. If $u$ is not a root of any nonzero $f \in K[x]$, $u$ is said to be transcendental over $K$.
Now, this book says: $\pi$ and $e$ are algebraic over $\mathbb R$, while transcendental over $\mathbb Q$.
But is this true? How could a polynomial $f \in R[x]$ has a root as $\pi$ or $e$?