Right, so you have an application where you don't genuinely have a dictionary -- e.g., inserting items in a different order can result in a very different outcome even when all the keys are distinct, or even worse, inserting two keys and then removing a third can give entirely different results depending on the order in which you inserted the first two. (Or other arbitrary things depending on your application.) That can of course come up; it's just been quite confusing for me to see a fuzzy search scenario like this presented as a counterexample when (at least to me) the discussion seemed to be about proper mappings.