"outranks is an endorelation on the set of all crew members of the Enterprise, where (x, y) ∈ outranks if character x has a higher Star Fleet rank than y. Is outranks reflexive? No, since no officer outranks him/herself. Is outranks symmetric? No, since an officer cannot outrank an officer who in turn outranks him/her. Is outranks antisymmetric? Yes, since if one officer outranks a second, the second one cannot also outrank the first. Is outranks transitive? Yes, since if one officer outranks a second, and that officer outranks a third, the first obviously also outranks the third. Is outranks a partial order? No, but close. It satisfies antisymmetry and transitivity, which are crucial. The only thing it doesn’t satisfy is reflexivity, since none of the members appear with themselves. If we changed this relation to ranksAtLeastAsHighAs, then we could include these “double” pairs and have ourselves a partial order."