  Sets are just extensional entities with particular multiplicity properties (that mark them off from multisets) and certain functionalities (that mark them off from functions-in-extension, graphs etc). Among the variety of objects in the extensional canon, sets are distinguished by their almost complete absence of structure. This points to one of the most perplexing but prominent rôles of set theory in modern mathematics. Almost any (indeed many people believe literally any) fact in mathematics can be construed as a fact about sets.