his degree of preference of to , we could summarize this information by any triplet of numbers satisfying the two inequalities: and .

If and were sums of money, the agent could vary the sum of money represented by until he could tell us that he found his degree of preference of over the revised amount equal to his degree of preference of over . If he finds such a , then the results of this last operation would be expressed by any triplet of numbers satisfying the relationships and . Any two triplets obeying these relationships