I have tried long and hard to find a real-world occurrence of a preorder relation which is not a partial order, but couldn't find any.
Can someone give a real-world example of a such a relation, that is, a relation which is reflexive and transitive but not antisymmetric?
By "real-world" I don't mean that it cannot be abstract; but it shouldn't be contrived. Examples from mathematics / physics / computer science / etc. are all elligible, as long as they occur naturally.