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.

Read more about this topic:  Empty Product

Famous quotes containing the word product:

    In fast-moving, progress-conscious America, the consumer expects to be dizzied by progress. If he could completely understand advertising jargon he would be badly disappointed. The half-intelligibility which we expect, or even hope, to find in the latest product language personally reassures each of us that progress is being made: that the pace exceeds our ability to follow.
    Daniel J. Boorstin (b. 1914)