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Ordered Pair

For any sets and , the ordered pair is the set $\{\{a\}, \{a,b\}\}$ .

The characterizing property of an ordered pair is:

$\displaystyle (a,b) = (c,d) \iff a=b$ and $\displaystyle c=d,$

and the above construction of ordered pair, as weird as it seems, is actually the simplest possible formulation which achieves this property.