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A set is an arbitrary collection of objects. The axiom of union allows one to combine the objects in many different sets and make them members of a single new set. It says one can go down two levels taking not the members of a set, but the members of members of a set and combine them into a new set.
This says for every set there exists a set that is the union of all the members of . Specifically, for every that belongs to the union set there must be some set such that belongs to and belongs to .