second draft of this book
of this book
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A set is an arbitrary collection of objects. The axiom of union allows us to combine the objects in many different sets and make them members of a single new set. It says we 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 . For every that belongs to there must be some set such that belongs to and belongs to .