There are several equivalent formulations:

- The Cartesian product of nonempty sets is nonempty, even if the product is of an infinite family of sets.
- Given any set
*S*of mutually disjoint nonempty sets, there is a set*C*containing a single member from each element of*S*.*C*can thus be thought of as the result of ``choosing" a representative from each set in*S*. Hence the name.

Mon Feb 23 16:26:48 EST 1998