second draft of this book
of this book
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Before giving the axioms that will allow us to construct the integers we give the axiom of set theory that defines what we mean by `'. Without this axiom there would be little point in defining the integers or anything else. The axiom of extensionality tells us that sets are uniquely defined by their members.
means and have the same truth value or are equivalent. They are either both true or both false. It is the same as . This axiom says a pair of sets and are equal if and only if they have exactly the same members.