Put a collection of strings into a Bloom filter. It is interesting that the resulting data structure is independent of the ordering of the input strings and does not internally use an ordering of the strings, where "use an ordering" is left somewhat vague. What other data structures have these properties?
Original motivation was to create a string representing a collection of names such that no name is made more important (e.g., earlier in order) than another one. Kind of a digital equivalent of a group photo.