Hello,

I have found different definitions of Čech complex for sheaf $F$ od abelian groups on topological space $X$ with respect to the cover $\mathcal U$. One in Gelfand-Manin says to take product of $F(U_{i_0} \cap \ldots \cap U_{i_n})$ for all $n$-tuples of indices $(i_0, \ldots ,i_n)$, and one in Hartshorne says that one considers only stricly increasing indices $i_0 < \ldots < i_n$.

How can I see that cohomologies of these "two different" Čech complexes coincide?