Question on sheaves

Question

Can someone explain the object in point 2, (in the second answer) to this thread

Failure of isomorphisms on stalks to arise from an isomorphism of sheaves

in some more details. Please help.

Answer 1

A section of that sheaf over an open set $ U $ is a finite subset of U and a choice of integer for each element in that set. This clearly isn't the constant sheaf but clearly has stalk $\mathbb { Z} $ at every point.