| For example, when proving that every bounded nonempty set X of real numbers has a least upper bound a, one proceeds as follows. |
| For instance, the intersection of a fuzzy subset and its complement may be nonempty. |
| Note that the presence of a given column in a pre-cluster uniquely determines the contents and relative position of the rows which have nonempty entries in that column. |
| Constraints on the strategies are described by a nonempty, closed, convex set K, model which covers most cases of practical interest. |
