For a project I am working on, I need an example of a preorder (reflexive and transitive relation) that is neither symmetric (like an equivalence relation) nor antisymmetric (like less than or equal to), preferably a non-mathematical example, or at least one that is accessible to non-mathematicians.
Thanks for any ideas!
Order people alphabetically by name. This is reflexive and transitive but obviously not symmetric. It's not anti-symmetric either, because people can have the same name without being the same person (as anyone unlucky enough to have the same name as someone placed on a no-fly list can tell you).