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To understand the formal version of these axioms you have to
know in what order operations like 
(AND) and
(OR) are performed. This is determined by
precedence as described in Table 5.2. Subexpressions involving
are evaluated before
logical operations like or 
. Parenthesis 
and square brackets ![$[]$](img43.png){kind=small}
are used
to override standard precedence and to make clearer how an
expression is to be evaluated. The portion of an expression inside
parenthesis is evaluated first.
The clearest example of how set theory builds on the empty set
is the construction of the integers. The integer
1 is defined as the set containing the empty set. Two is defined as
the set that contains 1 and the empty set (or 0). Not surprisingly
3 is the set that contains 0, 1 and 2. In general 
is defined as the union of all the elements of 
plus itself. Thus will contain
elements as long as
contains elements.
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Next: Axiom of extensionality Up: Mathematical
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