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.
Read more about this topic: Empty Product
Famous quotes containing the word product:
“These facts have always suggested to man the sublime creed that the world is not the product of manifold power, but of one will, of one mind; and that one mind is everywhere active, in each ray of the star, in each wavelet of the pool; and whatever opposes that will is everywhere balked and baffled, because things are made so, and not otherwise.”
—Ralph Waldo Emerson (1803–1882)