Prop 2.8. If $X$ is a point, then $H_n(X)=0$ for $n>0$ and $H_0(X) \cong \mathbb{Z}$.

It is often very convenient to have a slightly modified version of homology for which a point has trivial Homology groups in all dimensions, including zero. This is e n (X) to be the homology groups done by defining the Reduced homology groups

Book – video

Reduced homology theory (axiomatized)