Let us look to mathematics for a better understanding of equality. There are two equality relations in mathematics, identity and equivalence. Identity implies that the two items are exact matches in all ways. Except for Professor Yang's calves in the cloning barn, there are no truly identical members of the UConn community. When we speak of equality, we are not striving for identity, but rather equivalence.
Equivalence means that members of a group are identical under a given relationship.
By using membership of a community as the equivalence relation, it follows that we, as human persons or members of the University community, are all equals. We know that treating others as less than ourselves is not acceptable behavior. Considering them as equals is progress, but we most move to the next level - greater than. Here we must diverge from our strict mathematical analogy. In mathematics, transitivity holds.