Databases organise, configure, and perform thing-and-people multiples in sets. Belonging, inclusion, participation, and membership: many of the relations that make up the material-social life of people and things can be formally apprehended in terms of set-like multiples stored in databases. Mid-20th century database design derived different ways of gathering, sorting, ordering, and searching data from mathematical set theory. The dominant database architecture, the relational database management system, can be seen as a specific technological enactment of the mathematics of set theory. More recent developments such as grids, clouds, and other data-intensive architectures apprehend ever greater quantities of data. Arguably, in emerging data architectures databases themselves are subsumed by even more intensive set-like operations. Whole databases undergo set-like transformations as they are aggregated, divided, filtered, and sorted. At least at a theoretical level, the mathematics of set theory, as philosophically rendered by Alain Badiou, can also suggest some explanations of how multiples expand, ramify, and split in databases. Badiou’s account locates forms of instability or incoherence inherent in any set-based doing of multiples in the relation between parts and elements, between inclusion and belonging. Against the grain of Badiou’s resolutely philosophical project, a set-theoretical account of databases might also point towards some vertiginous elements that elude regulation, norms, and representation.