Exercise 4.1.3 of Qing Liu's Algebraic Geometry and Arithmetic Curves asks of us to prove, given a normal Noetherian local scheme $X$ of dimension $2$ with closed point $s$, that $X \backslash \{ s \}$ is a non-affine Dedekind scheme.
However, a Dedekind scheme has dimension $1$ and Liu defines normal schemes to be irreducible, so by taking the reduced induced subscheme structure on $X$, which is integral, we see that the open subset $X \backslash \{ s \}$ must also have dimension $2$ and so cannot be Dedekind. Surely even if I relax the definition of normal scheme to include reducible schemes, the result wouldn't hold in the irreducible case anyway? Have I missed something?