I stumbled across the statement that for an integral scheme $X$ and an elements $f_1, \ldots, f_n \in {\cal O}_X^{\times}$, there is a symbol map, viz.,
$$ {\mathrm S} \colon \{ f_1,\ldots,f_n \} \mapsto [f_1=0, \ldots ,f_n=0] \in {\cal Z}^{n}(X \times \Delta^m). $$
To the best of my knowledge, it was written as above, but each $f_i$ cannot be $0$. What is wrong with my ${\mathrm{S}}$ above?
Further, it was written that this map ${\mathrm{S}}$ factors through the subgroup generated by $\{f, 1 - f\}$, i.e. the relations given in the definition of Milnor $K$-group. Is it obvious that the image of any element involving $\{f, 1-f\}$ lands in the boundary $\partial({\cal Z}^n(X \times \Delta^{m+1}))$?