I'm currently studying Algebraic Topology from Hatcher's book and from Mosher and Tangora. However, when I try to compute the homology of Eilenberg-Maclane spaces using the Hurewicz theorem, there seems to be a bit of a discongruence between them.
Hatcher states that the reduced homology is isomorphic to the homotopy groups in degree $i\leq n$, therefore we have $$H^i(K(G,n))=\begin{cases}\mathbb{Z}&i=0\\0&0<i<n\\G&i=n\\?&i>n\end{cases}$$We get an extra $\mathbb{Z}$ in degree zero because the difference between reduced and unreduced homology theory.
But, Mosher and Tangora state that it is an isomorphism in each degree $i\leq n$ for unreduced homology, which would make a significant difference: $$H^i(K(G,n))=\begin{cases}0&i<n\\G&i=n\\?&i>n\end{cases}$$
Can anybody help me out with this? I don't know which one I have to follow.
Not many spaces have $H_0 = 0$.
Mosher and Tangora are either thinking in terms of reduced homology, or not worrying about the $0$ case. Clearly, $H_0(K(G,n))= \mathbb{Z}$. Where specifically did you read that $H_0$ was also $0$ ?