Empty Product - Nullary Cartesian Product

Nullary Cartesian Product

Consider the general definition of the Cartesian product:

If I is empty, the only satisfying g is the empty function :

Thus, the cardinality of the Cartesian product of no sets is 1.

Under the perhaps more familiar n-tuple interpretation,

that is, the singleton set containing the empty tuple. Note that in both representations the empty product has cardinality 1.