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The integers are defined by an axiom that asserts the existence
of a set that contains *all* the integers.
is defined as the set containing
and having the property that if is in then is in
. To write this compactly we define some
notation. We use the integer 0 to represent the empty set. If we
have some set then we can construct a set containing
that is written as .

This says there exists a set that contains the empty set 0 and for every set that belongs to the set constructed as also belongs to .

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