I'm looking at Fraleigh's First Course in Abstract Algebra book, 7th. edition.
Theorem 22.4 states
Let F be a subfield of a field E, let alpha be any element of E, and let x be an indeterminate. The map Psi_alpha: F[x] --> E defined by Psi_alpha(n degree polynomial) = alpha plugged into the polynomial is a homomorphism.
I don't understand why this book keeps specifying that Psi_alpha(x) = alpha. Isn't this obvious from just plugging in alpha for the indeterminate?