Diversity on ℘ fin(X)

In tight-span theory, a diversity is a generalization of metric space where the metric is defined over the set
℘ fin(X) which is composed of finite subsets of X. In this paper we are going to generalize the results of D. Silvestru and C. Gosa to derive some sharp inequalities for the diameter diversity. This sharp inequality can be used to study models with diversity in a collective manner.