A weakly ordered set has a most one best element. True or false?
In a weakly ordered set, every element is related to every other element. Given any element y, any other element x A ∈ belongs to either the upper or lower contour set. Together with the indifference sets, the upper and lower contour sets partition the set X in various ways. Furthermore the upper and lower contour sets are nested. The details are given in the following exercises.