I am confused about Theorem 1.4.5, Example 1.6.4(b) in SGA 4.5, because here a covering of $U$ is
a finite family $\{U_i\to U\}$ of flat morphisms such that $\coprod U_i\to U$ is surjective $\qquad$ (1)
. But in the definition of fpqc topology everywhere else, a covering of $U$ is
a (not necessary finite) family $\{U_i\to U\}$ of flat morphisms such that $\coprod U_i\to U$ is fpqc $\quad$(2)
where fpqc means faithfully flat and every affine open of $U$ is the image of a quasicompact open of $\coprod U_i$.
I believe that definition (1) allows too many coverings, and I don't see a way to prove Theorem 1.4.5 using definition (1) (in the proof Deligne says we can formally reduce to affine case, but definition (1) is not good enough to do so).