When we calculate the density of states for an electron, in the standard way as done in statistical mechanics textbooks ( by integrating once over space, then integrating over $\theta$ and $\phi$ of the k-space,etc), we finally multiply a '2' as the spin degeneracy.
My question is, since the electron can be in an infinite number of states on the Bloch sphere, why are we just taking two states? I know that only two of the infinite number of states are orthogonal, but even if the huge number of states are non-orthogonal, why should not they contribute to an increase in the number of states?
I did not want to use the term degeneracy in the title, because degeneracy is defined as the dimension of the eigenspace of the degenerate eigenvalue, so that is of course two. What I want to know is, why are we taking only the orthogonal states?