 In many situations, it can be easy to apply the Hewitt–Savage zero–one law to show that some event has probability 0 or 1, but surprisingly hard to determine "which" of these two extreme values is the correct one.Continuing with the previous example, define

which is the position at step "N" of a random walk with the iid increments "X""n".The event { "S""N" = 0 infinitely often } is invariant under finite permutations.